ROBOTIC UPPER TRUNK SUPPORT DEVICE

Abstract

An upper trunk training system may include a connection module including an actuation link configured to be coupled to a user's trunk, an output link coupled to the actuation link, and a base frame configured to be coupled to the user's trunk. An upper trunk training system may include a variable stiffness module including a cam fixed to a cam shaft coupled to the base frame, a cam follower coupled to the base frame and biased toward the cam. An upper trunk training system may include a stiffness control module including a sun gear fixed to the cam shaft, a planetary gear coupled to the output link of the connection module and meshed with the sun gear, a ring gear meshed with the planetary gear, and an electric machine coupled to the ring gear to rotate the ring gear to increase a stiffness of the upper trunk training system.

Claims

1. An upper trunk training system, comprising: a connection module including an actuation link configured to be coupled to a user's trunk, an output link coupled to the actuation link, and a base frame configured to be coupled to the user's trunk; a variable stiffness module including a cam fixed to a cam shaft coupled to the base frame, a cam follower coupled to the base frame and biased toward the cam; and a stiffness control module including a sun gear fixed to the cam shaft, a planetary gear coupled to the output link of the connection module and meshed with the sun gear, a ring gear meshed with the planetary gear, and an electric machine coupled to the ring gear to rotate the ring gear to increase a stiffness of the upper trunk training system.

2. The upper trunk training system of claim 1, wherein the connection module and the user's trunk form a four-bar linkage with a single degree-of-freedom.

3. The upper trunk training system of claim 1, wherein the cam includes a zero-support region, a force-matching region, a motion-restriction region, and a transition region.

4. The upper trunk training system of claim 1, wherein the cam follower includes a follower roller engaged with the cam.

5. The upper trunk training system of claim 1, wherein the cam follower includes a spring biasing the cam follower toward the cam.

6. The upper trunk training system of claim 5, wherein the spring is adjustable so that the stiffness of the upper trunk training system can be changed.

7. The upper trunk training system of claim 1, wherein the cam follower includes a potentiometer that provides displacement information indicative of a displacement of the cam follower, and wherein operation of the electric machine is based on the displacement information.

8. The upper trunk training system of claim 1, wherein the sun gear and the ring gear are coaxial with the cam shaft.

9. The upper trunk training system of claim 1, wherein the planetary gear includes three planetary gears all coupled to the output link.

10. The upper trunk training system of claim 1, wherein the output link is rotatably mounted to the cam shaft.

11. The upper trunk training system of claim 1, wherein the stiffness control module further includes: a driven gear rigidly mounted to the ring gear, and a worm gear coupled to the electric machine and meshed with the driven gear.

12. The upper trunk training system of claim 11, wherein the driven gear is coaxial with the cam shaft.

13. The upper trunk training system of claim 1, wherein the stiffness of the upper trunk training system is defined by the variable stiffness module when the electric machine is not moving, and wherein the stiffness of the upper trunk training system is defined by both the variable stiffness module and the stiffness control module when the electric machine is moving.

14. The upper trunk training system of claim 1, wherein the electric machine modulates the stiffness of the upper trunk training system based on a speed of rotation of the electric machine.

15. The upper trunk training system of claim 1, wherein the electric machine is a stepper motor.

16. An upper trunk training system comprising: a four-bar linkage configured to be coupled to a user's trunk; a cam shaft coupled to the four-bar linkage; a cam fixed to the cam shaft for rotation therewith; a cam follower coupled to the four-bar linkage and including a cam roller in contact with the cam; a spring biasing the cam follower toward the cam; a sun gear fixed to the cam shaft for rotation therewith; three planetary gears coupled to the four-bar linkage and meshed with the sun gear; a ring gear meshed with the three planetary gears; and a stepper motor coupled to the ring gear to rotate the ring gear to modulate a stiffness of the upper trunk training system.

17. The upper trunk training system of claim 16, wherein the four-bar linkage includes a base from supporting the cam shaft and an output link including a carrier mounted to the three planetary gears.

18. The upper trunk training system of claim 16, further comprising: a driven gear coupled to the ring gear; and a worm gear driven by the stepper motor and meshed with the driven gear.

19. The upper trunk training system of claim 16, wherein the cam includes a zero-support region, a force-matching region, a motion-restriction region, and a transition region.

20. An upper trunk training system comprising: an actuation link configured to be coupled to an upper portion of a user's trunk; an output link rotatably coupled to the actuation link; a base frame configured to be coupled to a lower portion of the user's trunk; and a parallel elastic actuator coupled between the output link and the base frame, the parallel elastic actuator including: a cam shaft, a cam fixed to the cam shaft for rotation therewith a cam follower coupled to the base frame and including a cam roller in contact with the cam; a spring biasing the cam follower toward the cam; a sun gear fixed to the cam shaft for rotation therewith; three planetary gears coupled to the output link and meshed with the sun gear; a ring gear meshed with the three planetary gears; and a stepper motor coupled to the ring gear to rotate the ring gear to modulate a stiffness of the upper trunk training system.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0025] The device is explained in even greater detail in the following drawings. The drawings are merely exemplary and certain features may be used singularly or in combination with other features. The drawings are not necessarily drawn to scale.

[0026] FIG. 1 is a perspective view of an upper trunk training system mounted on a patient simulator module, according to some implementations.

[0027] FIG. 2A is a perspective view of a stiffness control module of the upper trunk training system of FIG. 1, according to some implementations.

[0028] FIG. 2B is a section view of the stiffness control module of FIG. 2A, according to some implementations.

[0029] FIG. 2C is a section view of the stiffness control module of FIG. 2A, according to some implementations.

[0030] FIG. 3 is a side view of a variable stiffness module of the upper trunk training system of FIG. 1, according to some implementations.

[0031] FIG. 4 is a perspective view of the upper trunk training system of FIG. 1 attached to a user's trunk, according to some implementations.

[0032] FIG. 5 is a side view of the patient simulator module of FIG. 1, according to some implementations.

[0033] FIG. 6 is a schematic diagram of a connection module of the upper trunk training system of FIG. 1, according to some implementations.

[0034] FIG. 7 is a graph showing a relationship of a parallel elastic actuator output torque and the output link angle with a user trunk angle, according to some implementations.

[0035] FIG. 8 is a schematic diagram of the stiffness control module of FIG. 2A, according to some implementations.

[0036] FIG. 9A is a schematic representation of a cam profile of the variable stiffness module of FIG. 3, according to some implementations.

[0037] FIG. 9B is a schematic representation of a rotation motion of the cam profile of FIG. 9A, according to some implementations.

[0038] FIG. 10 is a schematic representation of a cam profile generation model, according to some implementations.

[0039] FIG. 11 is a graph showing output torque of the variable stiffness module of FIG. 3, according to some implementations.

[0040] FIG. 12 is a photograph of an experimental setup of the upper trunk training system of FIG. 1, according to some implementations.

[0041] FIG. 13 is a schematic representation of the driven torques of the patient simulator module of FIG. 1, according to some implementations.

[0042] FIG. 14A is a graph showing support torque vs. trunk angle of the upper trunk training system of FIG. 1, according to some implementations.

[0043] FIG. 14B is a graph showing torque error vs. trunk angle of the upper trunk training system of FIG. 1, according to some implementations.

[0044] FIG. 15A is a graph showing support torque error .sub.ROB,err,m(.sub.i) with respect to trunk angle .sub.i under different experimental conditions including experimental results of Group I (m=1,2) with different {dot over ()}, according to some implementations.

[0045] FIG. 15B is a graph showing support torque error .sub.ROB,err,m(.sub.i) with respect to trunk angle .sub.i under different experimental conditions including experimental results of Group II (m=3,4) with different m.sub.2, according to some implementations.

[0046] FIG. 15C is a graph showing support torque error .sub.ROB,err,m(.sub.i) with respect to trunk angle .sub.i under different experimental conditions including experimental results of Group III (m=5, 6, 7) with different .sub.cam,ini. The points A, B, and C in (c) indicate that .sub.ROB,err,m decreases with the variable stiffness module output torque .sub.VSMOD that are 5.71 Nm, 3.94 Nm, and 2.78 Nm, respectively, at the same trunk angle =74.7 Degrees, according to some implementations.

[0047] FIG. 15D is a graph showing support torque error .sub.ROB,err,m(.sub.i) with respect to trunk angle .sub.i under different experimental conditions including support torque errors .sub.ROB,err,m(.sub.i) (m=5, 6, 7) with respect to the cam angle .sub.cam in Group III. Error bars represent variations of the two repeated trials.

[0048] FIG. 16A is a free body diagram of a planetary gear system of the stiffness control module of FIG. 2A, according to some implementations.

[0049] FIG. 16B is a free body diagram of a sun gear of the planetary gear system of FIG. 16A, according to some implementations.

[0050] FIG. 16C is a free body diagram of a ring gear of the planetary gear system of FIG. 16A, according to some implementations.

[0051] FIG. 17A is a graph showing a comparison of support torque errors using original and modified ROBUTS output torque models under different experimental conditions including m=1 ({dot over ()}=0.6 Deg/s, m.sub.2=15 kg, .sub.cam,ini=0 Deg), according to some implementations.

[0052] FIG. 17B is a graph showing a comparison of support torque errors using original and modified ROBUTS output torque models under different experimental conditions including m=2 ({dot over ()}=0.9 Deg/s), according to some implementations.

[0053] FIG. 17C is a graph showing a comparison of support torque errors using original and modified ROBUTS output torque models under different experimental conditions including m=4 (m.sub.2=12 kg), according to some implementations.

[0054] FIG. 17D is a graph showing a comparison of support torque errors using original and modified ROBUTS output torque models under different experimental conditions including m=6 (.sub.cam,ini=20 Deg), according to some implementations.

[0055] FIG. 17E is a graph showing a comparison of support torque errors using original and modified ROBUTS output torque models under different experimental conditions including m=7 (.sub.cam,ini=40 Deg), according to some implementations.

[0056] FIG. 17F is a graph showing support torque evaluation results, according to some implementations.

DETAILED DESCRIPTION

[0057] Following below are more detailed descriptions of concepts related to, and implementations of, methods, apparatuses, and systems for a robotic upper trunk support. Before turning to the figures, which illustrate certain exemplary embodiments in detail, it should be understood that the present disclosure is not limited to the details or methodology set forth in the description or illustrated in the figures. It should also be understood that the terminology used herein is for the purpose of description only and should not be regarded as limiting.

[0058] Patients with trunk control impairment cannot perform many daily activities, which greatly reduces their life quality. Robotic devices are developed for trunk training, but human-machine interactions, such as support force control and joint misalignments, are not well-handled in current designs. In this work, a novel trunk training device called Robotic Upper Trunk Support (ROBUTS) 50 is developed to provide customized support forces in upper-trunk stabilization training, where a parallel elastic actuator with passive and active modules is used to control the forces: a passive elastic module using a cam-spring mechanism is designed to provide a baseline of the support force, and an active control module is designed for the force adjustment. A linkage mechanism is used to avoid joint misalignment between the ROBUTS and trunk. A kinematic model and a modified mechanic model of the ROBUTS are developed and used in the output torque control, where the actuator's motor angle is generated by the models to output a desired torque at a given trunk posture. A mechanism of the friction torque in the planetary gear set is proposed, which illustrates differences of the ROBUTS' output torque when the trunk moves back and forth. Experimental results show that the output torque has good repeatability and accuracy, and desired output torque control of the ROBUTS can be achieved with use of the modified model.

[0059] Trunk control needs coordination between the motor and nervous systems. Trunk control impairment has significant effects on the activities of daily living (ADLs) of patients. Thus, trunk training becomes a demand for patients to regain their functional ability. Robot-aided training devices can offer intensive, long-during, and repetitive training for patients.

[0060] Based on the Slacking Hypothesis, motor-learning outcomes of human bodies can be decreased if excessive support is provided. Thus, different from the position control strategy that is used in the typical trunk-support devices, the support force provided by devices discussed herein are actively adjusted based on the patient's muscle strength. To implement force control and increase compliance of human-machine interaction, different types of elastic actuators are developed, including parallel elastic actuators (PEAs) and serial elastic actuators (SEAs). The elastic actuators have low output impedance.

[0061] As shown in FIG. 1, the trunk training device called Robotic Upper Trunk Support (ROBUTS) 50 is developed for upper-trunk stabilization training in the sagittal plane with friendly human-machine interactions. The ROBUTS 50 is shown mounted on a patient simulation module (PSMOD) 52. The ROBUTS 50 can provide controllable support forces to implement customized and compliant assistance to patients with insufficient muscle strength. In the ROBUTS 50, a PEA 54 is designed to generate forces that are mainly provided by a passive elastic component and adjusted by a motor actuator. The elastic component of the PEA 54 is made of a variable stiffness module 58, of which the passive output torque itself can hold the whole weight of the upper trunk. The passive output torque is the baseline of the real output torque that is generated by the actuator in the PEA 54, which can reduce the control effort of the actuator. To avoid joint misalignment, a four-bar linkage mechanism is designed in the ROBUTS 50. Kinematic and mechanic models of the ROBUTS 50 have been developed, and a prototype of the device with a phantom model of the trunk is fabricated, which is used to test the support torque accuracy of the ROBUTS 50.

[0062] Based on data analysis, a primary source of the errors in the ROBUTS 50 is the friction torque of a planetary gear set in the PEA 54. Sliding friction of meshed spur gears has been modeled by Coulomb models with constant, time-varying, and empirical friction coefficients, which are related to gear mesh properties, lubricant conditions, and time-varying stiffness. For the planetary gear set, the sliding friction was studied by linear friction models with time-varying stiffness and spalling defects. Based on the Coulomb friction model, a mechanism of friction torque is proposed for the planetary gear set, which illustrates differences in the ROBUTS 50 output torque when the trunk moves back and forth. Based on the mechanism, a friction torque model that considers periodically varied friction arms is proposed to modify the original mechanic model of the ROBUTS 50. Parameter identification of the modified model is conducted, and experimental results show that the support torque accuracy is significantly improved by the modified model.

[0063] The PEA 54 of the ROBUTS 50 a variable stiffness module (VSMOD) 58 and a stiffness control module (SCMOD) 62, which work as the passive and active inputs, respectively, to generate an output torque on the trunk via a connection module (CONMOD) 64 including an output link (OLINK) 66, an actuation link 70, and a base frame 146. Input torque of the actuation link 70 comes from the output link 66, and it is transferred to the trunk via a four-bar linkage mechanism, where the patient trunk is modeled as a rotational link. The personalized passive support on the output link 66 is achieved by the VSMOD 58 with a customized cam profile design, and the support force can be actively controlled by changing the stiffness of the VSMOD 58 through a stepper motor in the SCMOD 62.

[0064] As shown in FIGS. 2A-C, the SCMOD 62 is the active part of the PEA 54, and includes a planetary gear set assembly 74 and a an electric machine in the form of a motor assembly 78. In the planetary gear set 74, a sun gear 82 is connected with a cam 86 of the VSMOD 58 through a cam shaft 90, a carrier 94 is fixed with the output link 66 as the output of the PEA 54, and a ring gear 98 is connected with a worm gear 102 of the motor assembly 78 via a coupler 107 and a driven gear 108, which is controlled by an electric machine in the form of a stepper motor 106 that connects to the worm gear 102. Planetary gears 110 are coupled to the carrier 94 between the sun gear 82 and the ring gear 98. When the stepper motor 106 stops, the ring gear 68 is fixed, and the stiffness of the output link 66 is unchanged and proportional to that of the cam 86. When the stepper motor 106 moves, the stiffness of the output link 66 is modulated by an additional rotation angle of the carrier 94 due to the rotation of the ring gear 98.

[0065] As shown in FIG. 3, the VSMOD 58 is the passive component of the PEA 54, and includes a cam-follower mechanism 114 and a spring 118 to provide passive forces. A follower roller 122 contacts the cam 86, and the spring compression force is transferred to the cam 86 through the cam-follower mechanism 114. The stiffness of the cam 86 (e.g., its torque-angle relationship on the cam shaft) can be generated by the design of the cam profile, which is customized based on the patient's requirements. In addition, linear bearings 126 are used to guide the motion of the cam-follower mechanism 114, screws 130 at a spring base 134 are used to adjust the initial compression of the spring 118, and a potentiometer 138 is used to measure the compression of the spring 118.

[0066] As shown in FIG. 4, the actuation link 70 (i.e., Link1) is the bridge between the patient trunk and the PEA 54 via the output link 66 (i.e., Link4). In some implementations, the actuation link 70 is a planar linkage mechanism connected to the patient trunk. When the patient trunk 142 is modeled as a rigid link called Link2 that rotates about the lumbar joint, a four-bar linkage mechanism can be formed where a base frame 146 of the ROBUTS 50 is Link3, which represents the fixed link connecting the lumbar joint and the center of the cam shaft 90. The kinematic relationship of the single degree-of-freedom four-bar linkage mechanism can be used to avoid joint misalignment problems.

[0067] As shown in FIG. 5, a phantom model of the upper trunk, which is called the patient simulation module (PSMOD) 52, is developed here to simulate the motion of an upper trunk 142 and used to evaluate the interaction between the ROBUTS 50 and trunk 142 before human experiments. The PSMOD 52 is made up of an upper trunk structure 150 and an actuation mechanism 154, which form a rocker-slider mechanism. The upper trunk structure 150 includes a rigid link 158 and weights 162 that simulate the bending motion and mass property of the trunk 142, respectively. The actuation mechanism 154 involves a linear actuator 166 that connects the base frame 146 and upper trunk structure 150 with revolute joints 170 at two ends. The linear actuator 166 can control the rotation of the upper trunk structure 150, and a load cell 174 is used to measure the support force for the trunk.

[0068] Modeling of the CONMODKinematic modeling and force analysis

[0069] The patient trunk 142 (Link2), base frame 146 (Link3), and links of the actuation link 70 and output link 66 (Link1 and Link4) form a single-DoF four-bar linkage system, and its schematic diagram is shown in FIG. 6. The origin O of the reference frame O-xy is set to be the intersection point of the horizontal line passing the lumbar joint and the vertical line passing the cam shaft 90 of the ROBUTS 50, the angle is the posture angle of the patient trunk, and r.sub.i, m.sub.i, C.sub.i (i=1, 2, 4) are the length, mass, and COM of the corresponding links, respectively. The patient's muscle strength (i.e., the active torque from the muscle) is denoted as .sub.a, which is simulated by the driven torque of the actuation mechanism in the PSMOD 52, and the torque provided by the PEA 54 is denoted as .sub.4. In the schematic diagram of FIGS. 6, r.sub.1, r.sub.2, r.sub.3, and r.sub.4 represent lengths of Link1, Link2 (trunk), Link3 (base frame) and Link4 (OLINK), respectively, E represents the center of the cam shaft, D represents the lumbar joint, and O-xy is the reference frame.

[0070] The kinematic constraints of the linkage mechanism can be expressed as:

[00001]$\begin{array}{cc}{x}_3+r_2\cos =r_1\cos {}_1+r_4\cos {}_4& \left(1\right)\end{array}$$\begin{array}{cc}{y}_3-r_2\sin =r_1\sin {}_1-r_4\sin {}_4& \left(2\right)\end{array}$

where .sub.1 and .sub.4 are the angles of Link1 and Link4, respectively, as shown in FIG. 6, x.sub.3 is the horizontal distance between the lumbar joint and the origin of the reference frame, y.sub.3 is the vertical distance between the cam shaft and origin of the reference frame, and r.sub.3={square root over (x.sub.3.sup.2+y.sub.3.sup.2)} is the length of the base frame (Link3). If any one of , .sub.1 and .sub.4 is given, the other two angles can be calculated by (1) and (2). At a given trunk angle , the relationship between .sub.4 and .sub.a can be obtained by the principle of virtual work when the trunk system is in a quasi-static state:

[00002]$\begin{array}{cc}W=0=m_{2}g\left(\stackrel{\_}{D{C}_2}\sin \right)+m_{4}g\left(\stackrel{\_}{E{C}_4}\sin {}_4\right)-{}_a-{}_4{}_4+m_{1}g\left(r_2\sin +\stackrel{\_}{A{C}_1}\sin {}_1\right)& \left(3\right)\end{array}$

[0071] Taking variations of (1) and (2) and substituting resultant equations into (3) yield

[00003]$\begin{array}{cc}{\stackrel{}{}}_4=-\frac{{}_a}{f_4\left(\right)}+\frac{m_{1}g\stackrel{\_}{{\mathrm{AC}}_1}\cos {}_I{f}_1\left(\right)}{f_4\left(\right)}+\frac{m_1{\mathrm{gr}}_2\cos }{f_4\left(\right)}+\frac{m_{2}g\stackrel{\_}{{\mathrm{DC}}_2}\cos }{f_4\left(\right)}+m_{4}g\stackrel{\_}{{\mathrm{EC}}_4}\cos {}_4& \left(4\right)\end{array}$

where .sub.4 is the required torque of .sub.4, .sub.1, and .sub.4 are functions of given by (1) and (2), f.sub.1()=.sub.1/, and f.sub.4()=.sub.4/. In a quasi-static state, the PEA output torque .sub.4 is equal to the required torque .sub.4, which can be calculated by (4) if the patient's active torque .sub.a is given at a trunk angle .

[0072] The support torque of the ROBUTS 50 is denoted by .sub.ROB, which is applied on the lumbar joint of the trunk (Link2). The support torque .sub.ROB is transferred from the PEA output torque .sub.4 through the actuation link 70. Based on the kinematic relationship in (1) and (2), the ROBUTS support torque can be calculated as

[00004]$\begin{array}{cc}{}_{\mathrm{ROB}}={}_4{f}_4\left(\right)& \left(5\right)\end{array}$

Modeling of the CONMODLink Lengths Optimization

[0073] To minimize the peak value of .sub.4, an optimization problem is defined here to find the optimized lengths of r.sub.1 and r.sub.4 in the actuation link 70. The objective function is

[00005]$\begin{array}{cc}\underset{r_1,r_4}{\min }\left\{\underset{}{\max }\left({}_4\right)\right\}& \left(6\right)\end{array}$$\mathrm{such}\mathrm{that}$$\begin{array}{cc}0.05m{r}_{1}0.4m& \left(7\right)\end{array}$$0.05m{r}_{4}0.4m$$\begin{array}{cc}60\mathrm{Deg}90\mathrm{Deg}& \left(8\right)\end{array}$${}_{4}90\mathrm{Deg}$${}_1+180\mathrm{Deg}$

where length ranges of Link1 and Link4 are defined in (7), and the predefined workspace of the trunk, angle ranges of Link4, and a singular configuration boundary of Link1 and Link2 are defined in (8). Besides, r.sub.2=0.400 m, x.sub.3=0.150 m, and y.sub.3=0.500 m are the predefined geometric parameters. In the calculation of .sub.4, the patient active torque .sub.a=0 Nm is adopted to obtain the maximum .sub.4. Based on the human body segment parameters, the trunk mass is m.sub.Trunk=m.sub.2=33.725 kg and the COM of the trunk is located at l.sub.C,Trunk=DC.sub.2=0.357 m. The optimized lengths of Link1 and Link4 are

[00006]$\begin{array}{cc}{r}_1=0.295m,r_4=0.155m& \left(9\right)\end{array}$

[0074] Using the optimized lengths in (9), the PEA's maximum output torque .sub.(4,max) is 22.346 Nm, which happens when the trunk bends to =60.9 Deg, as shown in FIG. 7. The OLINK angle .sub.4 changes from 24.163 Deg to 89.386 Deg when the trunk moves from 60.9 Deg to 90 Deg, i.e., the trunk motion is amplified over twice on the OLINK, as shown in FIG. 7. In addition, the singular configuration of Link1 and Link4 happens at =50.9 Deg when they are collinear, and this configuration works as a safety limit to prevent the trunk from bending further. The torque curve shown in FIG. 7 suggests that the relationship between the PEA output torque and trunk angle is nonlinear. Relationships of the PEA output torque and the OLINK angle with the patient's trunk angle. The workspace of the trunk is defined between =60.9 Deg and =90 Deg, and a restricted-workspace of the trunk is defined between =50.9 Deg and =60.9 Deg.

Modeling of the SCMOD

[0075] The SCMOD 62 consists of the planetary gear set assembly and the motor assembly, whose schematic diagram is shown in FIG. 8. In the motor assembly, the stepper motor is connected with the worm and the ring gear is fixed with the worm gear. Thus, the relationship of the angular velocities of the motor .sub.motor and ring gear .sub.ring is

[00007]$\begin{array}{cc}{}_{\mathrm{ring}}=\frac{1}{N_{\mathrm{wg}}}{}_{\mathrm{motor}}& \left(10\right)\end{array}$

where N_wg is the gear ratio of the worm and worm gear. In the planetary gear set assembly, the carrier and sun gear are connected with the OLINK and cam, respectively, and the kinematic relationship of the planetary gear set is

[00008]$\begin{array}{cc}{}_{\mathrm{cam}}=\frac{N_{\mathrm{sun}}+N_{\mathrm{ring}}}{N_{\mathrm{sun}}}{}_4-\frac{N_{\mathrm{ring}}}{N_{\mathrm{sun}}}{}_{\mathrm{ring}}& \left(11\right)\end{array}$

where _cam and _4 are angular velocities of the cam and OLINK, respectively, and N_ring and N sun are teeth numbers of the ring gear and sun gear, respectively.

[0076] The torque on the sun gear transferred from the cam, .sub.VSMOD (.sub.cam), is a function of the cam angle .sub.cam, which is determined by the cam profile shown in the following section. Based on (11), the PEA output torque .sub.4 on the OLINK is proportional to .sub.VSMOD(.sub.cam) when the motor does not move:

[00009]$\begin{array}{cc}{}_4=-\frac{N_{\mathrm{sun}}+N_{\mathrm{ring}}}{N_{\mathrm{sun}}}{}_{\mathrm{VSMOD}}\left({}_{\mathrm{cam}}\right)& \left(12\right)\end{array}$

Substituting (10) into (11) and integrating the resultant equation yield

[00010]$\begin{array}{cc}{}_{cam}=\frac{N_{\mathrm{sun}}+N_{\mathrm{ring}}}{N_{\mathrm{sun}}}\left({}_4-{}_{4,0}\right)-\frac{N_{\mathrm{ring}}}{N_{\mathrm{sun}}}\frac{1}{N_{\mathrm{wg}}}{}_{\mathrm{motor}}& \left(13\right)\end{array}$

where .sub.cam, .sub.4, and .sub.motor are current angles of the cam, OLINK, and motor, respectively, and .sub.4,0 is the initial angle of the OLINK. Initial angles of the motor and cam are set to be zero when the trunk is at the vertical posture (=90 Deg). Based on (13), the relationship between .sub.4 and .sub.cam is changed when the motor moves. Combining (12) and (13), the PEA output torque .sub.4 is a function of .sub.4 and .sub.motor

[00011]$\begin{array}{cc}{}_4=f_{\mathrm{PEA}}\left({}_4,{}_{\mathrm{motor}}\right)=-\frac{N_{sun}+N_{\mathrm{ring}}}{N_{sun}}{}_{\mathrm{VSMOD}}\left(\frac{N_{sun}+N_{\mathrm{ring}}}{N_{sun}}\left({}_4-{}_{4,0}\right)-\frac{N_{\mathrm{ring}}}{N_{\mathrm{sun}}}\frac{1}{N_{\mathrm{wg}}}{}_{\mathrm{motor}}\right)& \left(14\right)\end{array}$

where f.sub.PEA is the torque-angle relationship of the PEA. From (14), the PEA output torque .sub.4 can be modulated by the motor angle .sub.motor since it changes .sub.cam even if .sub.4 is unchanged.

Modeling of the VSMOD

[0077] A special design of the cam profile is developed to match the reference torque that can hold a trunk at all postures. The cam profile is divided into four regions: the zero-support region, force-matching region, motion-restriction region, and transition region, as shown in FIGS. 9A and 9B. The profile of the zero-support region is an arc that its center coincides with that of the cam shaft, where the spring of the VSMOD is not compressed and no output torque will be generated. The profile of the force-matching region is designed to provide the support force that can passively hold the trunk at all postures. The motion-restriction region is used to generate a large resistant force to stop the motion of the trunk. The transition region is the connection of the motion-restriction and zero-support regions.

[0078] As shown in the schematic diagrams of FIGS. 9A and 9B, the customizable cam profile, where O.sub.c-x.sub.cr y.sub.cr is the cam's reference frame with O.sub.c coincident with the center of the cam shaft and axes parallel to those of the global reference frame Oxy, .sub.fm and .sub.zs are sector angles of the force-matching and zero-support regions, respectively, the start configuration position (STCON) and the limit configuration position (LMTCON) are the boundaries of the zero-support region, Q.sub.0 is the roller center at STCON with O.sub.cQ.sub.0=y.sub.0 being the distance from O.sub.c, and P.sub.0 is the corresponding contact point of the cam and roller. (b) The schematic diagram of the cam rotation motion, where Q is the roller center at the current configuration with O.sub.cQ=y being the distance from O.sub.c, P is the corresponding contact point of the cam and roller, and the current configuration is defined by the cam angle .sub.cam that is measured from O.sub.cQ to O.sub.cQ.sub.0, where Q.sub.0 is the position of the roller center Q.sub.0 in the current configuration.

[0079] The working mode of the ROBUTS is related to the initial configuration of the cam follower mechanism. When the roller is initially placed at the connection of the zero-support and force-matching regions, i.e., the start configuration position (STCON), the ROBUTS works in the full support mode so that the trunk can be passively supported by the device with no active torque required from the patient. When the roller is initially placed at a position in the zero-support region, there is no output torque generated until the roller enters the force-matching region, and the ROBUTS works in a partial support mode. In this mode, there is a region that allows free motions of the trunk, which can increase training challenges. When the roller starts from the connection of the zero-support and transition regions, i.e., the limit configuration position (LMTCON), no output torque is generated by the ROBUTS if the motor does not move. Illustrations of the cam profile of the force-matching region and the motor-modulated VSMOD output torque are shown as follows.

Design of the Force-Matching Region

[0080] The cam profile of the force-matching region is designed to make .sub.4 generated by the PEA via (14) equal to the required torque given by (4), where the motor does not move:

[00012]$\begin{array}{cc}{\stackrel{}{}}_4=-\frac{N_{sun}+N_{\mathrm{ring}}}{N_{sun}}{\stackrel{\_}{}}_{\mathrm{VSMOD}}\left({}_{cam}\right),0{}_{cam}{}_{\mathrm{fm}}& \left(15\right)\end{array}$

where .sub.cam=(N.sub.sun+N.sub.ring)/N.sub.sun. (.sub.4.sub.4,0) is the current cam angle, as shown in FIG. 9B, .sub.VSMOD (.sub.cam) is the required torque of .sub.VSMOD in the force-matching region, and .sub.fm is the sector angle of the force-matching region. To generate the needed cam profile, the function .sub.VSMOD(.sub.cam) is used to the principle of virtual work of the cam-spring mechanism:

[00013]$\begin{array}{cc}{\stackrel{}{}}_{\mathrm{VSMOD}}{}_{cam}=F_{\mathrm{spr}}{x}_{\mathrm{spr}}& \left(16\right)\end{array}$

where F.sub.spr=k.sub.sprx.sub.spr is the spring force, k.sub.spr is the stiffness coefficient of the linear spring, x.sub.spr=yy.sub.0 is the spring compression, in which y and y.sub.0 are the distances between the roller center and cam center at the current position and initial position (STCON), respectively, as shown in FIG. 9B. Integrating (16) yields the trajectory of the roller center

[00014]$\begin{array}{cc}y\left({}_{cam}\right)=y_0+\sqrt{{}_{{}_{\mathrm{cam},0}}^{{}_{\mathrm{cam}}}\frac{2{\stackrel{}{}}_{\mathrm{VSMOD}}}{k_{\mathrm{spr}}}d{}_{\mathrm{cam}}}& \left(17\right)\end{array}$

[0081] To easily develop the cam profile, the computation's reference frame is changed from the cam's reference frame O.sub.cx.sub.cry.sub.cr to the body frame O.sub.cx.sub.cby.sub.cb, which is rotated with the cam. In the cam's body frame, the cam is fixed, and the roller rotates around the cam along its trajectory that is generated by (17), as shown in FIG. 10. The roller center Q when it reaches an angle of .sub.cam is

[00015]$\begin{array}{cc}\left[\begin{array}{c}{x}_Q\left({}_{cam}\right)\\ y_Q\left({}_{cam}\right)\end{array}\right]=\left[\begin{array}{c}y\left({}_{\mathrm{cam}}\right)\cos \left({}_{\mathrm{cam}}\right)\\ y\left({}_{\mathrm{cam}}\right)\sin \left({}_{\mathrm{cam}}\right)\end{array}\right]& \left(18\right)\end{array}$

Thus, the cam profile of the force-matching region is

[00016]$\begin{array}{cc}& \left(19\right)\end{array}$$\left[\begin{array}{c}{x}_P\left({}_{cam}\right)\\ y_P\left({}_{cam}\right)\end{array}\right]=\left[\begin{array}{c}{x}_Q\left({}_{cam}\right)\\ y_Q\left({}_{cam}\right)\end{array}\right]+r_{\mathrm{roller}}{\stackrel{.fwdarw.}{e}}_{n,Q}\left({}_{\mathrm{cam}}\right)=\left[\begin{array}{c}{x}_Q\left({}_{cam}\right)-r_{\mathrm{roller}}\frac{y_Q^{}}{\sqrt{x_Q^2+y_Q^2}}\\ y_Q\left({}_{cam}\right)+r_{\mathrm{roller}}\frac{y_Q^{}}{\sqrt{x_Q^2+y_Q^2}}\end{array}\right]$

where [x.sub.P(.sub.cam) y.sub.P(.sub.cam)].sup.T is the coordinates of the contact point P, r.sub.roller is the radius of the roller, {right arrow over (e)}.sub.n,Q(.sub.cam) is the normal direction of the roller trajectory at the current roller position Q, and [x.sub.Q y.sub.Q].sup.T is the derivative of [x.sub.Q(.sub.cam) y.sub.Q(.sub.cam)].sup.T with respect to .sub.cam.

Analysis of the Cam Torque

[0082] When the motor rotates, the roller can move into different regions of the cam profile to modulate the output torque of the VSMOD

[00017]$\begin{array}{cc}{}_{\mathrm{VSMOD}}=\{\begin{array}{cc}0,& -{}_{\mathrm{zs}}{}_{\mathrm{cam}}<0\\ {\stackrel{\_}{}}_{\mathrm{VSMOD}}\left({}_{\mathrm{cam}}\right),& 0{}_{\mathrm{cam}}<{}_{\mathrm{fm}}\\ \max \left({\stackrel{\_}{}}_{\mathrm{VSMOD}}\right),& {}_{\mathrm{fm}}{}_{\mathrm{cam}}<{}_{\mathrm{fm}}+{}_{mr}\end{array}& \left(20\right)\end{array}$

where .sub.VSMOD(.sub.cam) is the required output torque in the force-matching region given by (15), .sub.zs and .sub.mr are sector angles of the zero-support and motion-restriction regions, respectively, and max (.sub.VSMOD) is to find the maximum value of .sub.VSMOD. For the cam profile designed in this work, sector angles of the zero-support and motion-restriction regions are the same, i.e., .sub.zs=.sub.fm=156.5 Deg. Thus, the patient's trunk is able to move freely from the upright to the maximum bending posture if the roller is initially placed at the LMTCON.

[0083] As shown in the schematic diagram of FIG. 10, the cam profile generation model, where O.sub.cx.sub.cby.sub.cb is the cam's body frame, .sub..sub.cam and .sub..sub.cam.sub.,0 are cam's radii of curvatures at P and P.sub.0, respectively, and {right arrow over (e)}.sub.n,Q and {right arrow over (e)}.sub.t,Q are normal and tangential directions of the roller center trajectory at Q, respectively.

[0084] In the case that the motor does not move, there are three working modes. (a) If the roller is located at the STCON when the trunk is upright, the cam initial angle .sub.cam,ini=0 Deg, and the VSMOD works in the force-matching region when the trunk moves in its workspace, which is called the full-support mode, as shown in FIG. 11 with the solid red line. (b) If the roller is located at the LMTCON with the cam initial angle .sub.cam,ini=.sub.zs=156.5 Deg, there is no torque provided by the VSMOD, which is called zero-support mode, as shown in FIG. 11 with the solid black line. (c) If the roller is placed at the cam's zero-support region, for example, the cam initial angle is .sub.cam,ini=78 Deg, the trunk experiences a zero-support motion (75.3 Deg90 Deg), when the roller is in the zero-support region of the cam, and then a partial-support motion (60.9 Deg<75.3 Deg), when the roller is in the force-matching region, which is called partial-support mode, as shown in FIG. 11 with the solid blue line. When the motor moves, the output torque can be any value in the region that is enclosed by the curves of the zero- and full-support modes. Due to the restricted-workspace, the trunk can be held by the device even if it works in the partial-support and zero-support modes, as shown by the points B and C in FIG. 11, respectively.

Experiments and Discussions

Experimental Setup

[0085] FIG. 11 shows an exemplary VSMOD output torque in different modes. The region between the two solid green lines represents the restricted-workspace of the trunk, and the right side is the workspace of the trunk. The solid cyan line represents the needed torque to support a patient with no muscle strength. Point A (=75.3 Deg) corresponds to the trunk posture when the ROBUTS enters the cam's force-matching region when _(cam,ini)=78 Deg. Points B (=54.7 Deg) and C (=51.4 Deg) correspond to the trunk postures when the trunk is held by the ROBUTS in the restricted-workspace when _(cam,ini)=78 Deg and 156.5 Deg, respectively.

[0086] A ROBUTS prototype was built for the model validation and performance evaluation, as shown in FIG. 12. A linear actuator with a 250 mm stroke (ECO LLC, Boulder, CO, USA) was used as the actuation mechanism of the PSMOD to drive the upper trunk structure with a load cell DYLY-106-50 kg (Calt, Shanghai, China) to record the driven force. Gravity sensors ADXL345 (Sparkfun, Boulder, CO, USA) were fixed on Link4 (OLINK) of the CONMOD and the upper trunk structure of the PSMOD to record angles. Three increment encoders AMT 102-V (500 ppr, CUI DEVICES, Tualatin, OR, USA) were used to record the rotation angles of the motor and cam, and the angle changes between Link1 and Link4 of the CONMOD. A potentiometer KTC-50 mm (KTC, Shenzhen, Guangdong, China) was used to measure the displacement of the roller of the VSMOD. A stepper motor STP-MTR-23055 (SureStep, China) was used in the motor assembly of the SCMOD and it was driven at 12 V with PWM signals through a stepper motor driver TB6600 (DFROBOT, Shanghai, China). The signals from the above sensors were collected via Arduino Mega 2560 board (Arduino, Ivrea, Italy) and sent to a host PC. Bending motion tests were performed to evaluate the kinematic relationship of the ROBUTS prototype, which matched well with the kinematic model of the ROBUTS.

[0087] In the prototype, the ratio of the worm and worm gear assembly of the SCMOD was N.sub.wg=1/30, the gear teeth numbers of the planetary gear set assembly were N.sub.sun=60 and N.sub.ring=84, and the stiffness coefficient of the compression spring in the VSMOD was k.sub.spr=8.8 N/mm. The length parameters of the PSMOD were a.sub.1=0.100 m, a.sub.2=0.265 m, a.sub.3,x=0.500 m, a.sub.3,y=0.120 m, and a.sub.4=0.355 m+l.sub.s, where Is was the linear actuator's stroke length, as shown in FIG. 12. Thus, the driven torque .sub.ext of the actuation mechanism can be calculated as

[00018]$\begin{array}{cc}{}_{\mathrm{ext}}=f_{\mathrm{ext}}{l}_{\mathrm{ext}}\left(\right)& \left(21\right)\end{array}$

where f.sub.ext is the driven force obtained by the load cell and l.sub.ext() is the moment arm about the lumbar joint, as shown in FIG. 13.

Evaluation of the ROBUTS Support Torque Model

[0088] The support torque accuracy of the ROBUTS was tested in this section. When the trunk angle and motor angle _motor is acquired by sensors, the ROBUTS support torque .sub.ROB,mod can be calculated by the mechanic model of (5), (12), (13) and (20). The experimental support torque .sub.ROB,exp is obtained by the moment balance equation of the upper trunk structure about the lumbar joint:

[00019]$\begin{array}{cc}{}_{\mathrm{ROB},\exp }={}_g\left(\right)-{}_{\mathrm{ext}}& \left(22\right)\end{array}$

where .sub.g()=m.sub.2g cos is the gravity-induced torque, and .sub.ext is obtained by (21). The error of the ROBUTS support torque between .sub.ROB,mod and .sub.ROB,exp is

[00020]$\begin{array}{cc}{}_{\mathrm{ROB},\mathrm{err}}={}_{\mathrm{ROB},\mathrm{mod}}-{}_{\mathrm{ROB},\exp }& \left(23\right)\end{array}$

which is used to evaluate the accuracy of the ROBUTS mechanic model.

[0089] As shown in the schematic diagram of FIG. 13, the driven torque of the PSMOD. The base frame with a link length a.sub.3={square root over (a.sub.3,x.sup.2+a.sub.3,y.sup.2)}, the upper trunk structure with link lengths a.sub.1 and a.sub.2, and the linear actuator with a link length a.sub.4 form a four-bar linkage mechanism, where the trunk angle is measured by a gravity sensor and the driven force f.sub.ext is measured by a load cell. The force arm l.sub.ext () is calculated from the kinematic equation of the PSMOD with a given .

[0090] As shown in FIGS. 14A and 14B, (a) Comparison of the ROBUTS support torque between the model-predicted value .sub.ROB,mod (Mod) and experimental value .sub.ROB,exp (Exp), and the forward and backward bending processes are denoted by forward and backward, respectively. (b) The ROBUTS support torque error .sub.ROB,err during the forward and backward bending processes.

[0091] In the test, the angular velocity and mass of the upper trunk structure were {dot over ()}=0.6 Deg/s and m.sub.2=15 kg, respectively, and the cam initial angle of the VSMOD was .sub.cam,ini=0 Deg. The experiment was conducted in three steps: (a) the upper trunk structure was driven from the upright posture (=90 Deg) to a desired angle =70 Deg, which is the forward bending direction; (b) the upper trunk structure was rested for 5 s; (c) the upper trunk structure was driven back to the upright posture, which is the backward bending direction. The trunk angle , cam angle .sub.cam, and driven force f.sub.ext were recorded and used for the calculations of .sub.ROB,mod, .sub.ROB,exp and .sub.ROB,err. Results in FIG. 14A show that .sub.ROB,exp is significantly less than the model-predicted torque .sub.ROB,mod during the backward bending process, and there are obvious fluctuations in experimental torques of both directions. By observing the error .sub.ROB,err in FIG. 14B, the error fluctuations are in periodic patterns and the amplitudes increase with the support torque. Thus, the original mechanic model should typically be modified by the source of error.

[0092] The error .sub.ROB,err is mainly caused by the internal resistance related to relative motions of components in the ROBUTS. Three groups of experiments were designed to evaluate the effects of the three variables, trunk angular velocity {dot over ()}, trunk mass m.sub.2 and cam initial angle .sub.cam,ini, on the resistance. Note that the three variables are not considered as factors in the original mechanic model. The default values of the three variables are the same as those in the above test (FIGS. 14A and 14B). For the controlled test in each group, all three variables were the default values. For other in each group, one of the three variables was changed to different candidate values and the other two were the default values. Thus, the candidate values of the three groups are: I) in Group I, {dot over ()}=0.6 Deg/s, 0.9 Deg/s; II) in Group II, m.sub.2=15 kg, 12 kg, and III) in Group III, .sub.cam,ini=0 Deg, 20 Deg, 40 Deg. In total, there were seven experimental conditions, and tests of each experimental condition were repeated twice for repeatability test. The motor did not move during the tests.

[0093] For each experimental condition, the difference in the error between two repeated trials is computed as

[00021]$\begin{array}{cc}{}_{\mathrm{ROB},\mathrm{err},m}\left({}_i\right)={}_{\mathrm{ROB},\mathrm{err},m}^{\left(1\right)}\left({}_i\right)-{}_{\mathrm{ROB},\mathrm{err},m}^{\left(2\right)}\left({}_i\right)& \left(24\right)\end{array}$

[0094] where .sub.ROB,err,m.sup.(j)(.sub.i) is the ROBUTS support torque error at trunk angle .sub.i (i=1, 2, . . . , n) in the j-th(j=1,2) trial under experimental condition m(m=1, 2, . . . , 7), which is calculated by (23), and n is the number of measured trunk angles. Torque repeatability of the two trials can be evaluated by computing the mean (.sub.ROB,err,m) and standard deviation (SD, .sub.T,m) of .sub.ROB,err,m(.sub.i)

[00022]$\begin{array}{cc}{\stackrel{\_}{}}_{\mathrm{ROB},\mathrm{err},m}=\frac{{.Math.}_{i=1}^n{}_{\mathrm{ROB},\mathrm{err},m}\left({}_i\right)}{n}& \left(25\right)\end{array}$$\begin{array}{cc}{}_{,m}\sqrt{\frac{{.Math.}_{i=1}^n{\left({}_{\mathrm{ROB},\mathrm{err},m}\left({}_i\right)-{\stackrel{\_}{}}_{\mathrm{ROB},\mathrm{err},m}\right)}^2}{n-1}}& \left(26\right)\end{array}$

[0095] FIGS. 15A-15D. ROBUTS support torque error .sub.ROB,err,m(.sub.i) with respect to trunk angle .sub.i under different experimental conditions: (a) experimental results of Group I (m=1,2) with different {dot over ()}, (b) experimental results of Group II (m=3,4) with different m.sub.2, (c) experimental results of Group III (m=5, 6, 7) with different .sub.cam,ini. The points A, B, and C in (c) indicate that .sub.ROB,err,m decreases with the VSMOD output torque .sub.VSMOD that are 5.71 Nm, 3.94 Nm, and 2.78 Nm, respectively, at the same trunk angle =74.7 Deg. (d) ROBUTS support torque errors .sub.ROB,err,m(.sub.i) (m=5, 6, 7) with respect to the cam angle .sub.cam in Group III. Error bars represent variations of the two repeated trials.

[0096] Compared to the range of the ROBUTS support torque (032 Nm), the means and SDs of .sub.ROB,err,m(.sub.i) in the seven experimental conditions were all small, as shown in Table I. Thus, the repeatability is high, and the means of the two repeated trials under each experimental condition, .sub.ROB,err,m(.sub.i)=.sub.j=1.sup.2 .sub.ROB,err,m.sup.(j)(.sub.i), were used for the following error analysis. The mean errors .sub.ROB, err,m(.sub.i) with respect to trunk angle .sub.i in the above three groups were shown in FIGS. 15A-15C, respectively.

TABLE-US-00001 TABLE I .sub.ROB, err, m and .sub., m Under Different Experimental Conditions c Bending directions Condi- Forward Backward Groups tions .sub.ROB, err, m/ .sub.ROB, err, m/ (M) (m) Nm .sub., m/Nm Nm .sub., m/Nm I 1* 0.0631 0.8787 0.1604 0.6326 2 0.0354 2.7052 0.6912 1.2758 II 3* 0.0631 0.8787 0.1604 0.6326 4 0.2051 0.7863 0.1994 0.8021 III 5* 0.0631 0.8787 0.1604 0.6326 6 0.2014 0.7427 0.0857 0.5448 7 0.0693 0.5822 0.1361 0.4369 Note: Experimental conditions 1 and 2 correspond to the tests in Group I with {dot over ()} = 0.6 Deg/s and 0.9 Deg/s, respectively, experimental conditions 3 and 4 corresponds to the tests in Group II with m.sub.2 = 15 kg and 12 kg, respectively, and experimental conditions 5, 6 and 7 corresponds to the tests in Group III with .sub.cam, ini = 0 Deg, 20 Deg, and 40 Deg, respectively. Experimental conditions with * were the controlled conditions.

[0097] Effects of the three variables {dot over ()}, m.sub.2 and .sub.cam,ini on .sub.ROB were studied in Group I, II, and III, respectively. Taking Group I for example, since .sub.ROB,mod(.sub.i) is not affected by the three variables, the differences of the ROBUTS support torques at any trunk angle .sub.i is

[00023]$\begin{array}{cc}{}_{\mathrm{ROB},I}\left({}_i\right)={\stackrel{}{}}_{\mathrm{ROB},\mathrm{err},1}\left({}_i\right)-{\stackrel{}{}}_{\mathrm{ROB},\mathrm{err},2}\left({}_i\right)& \left(27\right)\end{array}$

The influence of {dot over ()} on .sub.ROB can be evaluated by the mean (.sub.ROB,I) and SD (.sub.T,I) of .sub.ROB,err,m(.sub.i):

[00024]$\begin{array}{cc}{\stackrel{\_}{}}_{\mathrm{ROB},I}=\frac{{.Math.}_{i=1}^n{}_{\mathrm{ROB},I}\left({}_i\right)}{n}& \left(28\right)\end{array}$$\begin{array}{cc}{}_{}\sqrt{\frac{{.Math.}_{i=1}^n{\left({}_{\mathrm{ROB},I}\left({}_i\right)-{\stackrel{\_}{}}_{\mathrm{ROB},I}\right)}^2}{n-1}}& \left(29\right)\end{array}$

[0098] The formulas of Group II and III are defined in the similar way, i.e., (.sub.ROB,II, .sub.,II) and .sub.ROB,III, .sub.,III), respectively. The influences of the three variables were different, as shown in FIGS. 15A-15C. For the tests with different {dot over ()} in Group I, .sub.ROB,I and .sub.,I were 0.1084 Nm and 0.6579 Nm, respectively, during the forward bending process, and .sub.ROB,I and .sub.,I were 0.2630 Nm and 1.1247 Nm, respectively, during the backward bending process, as shown in FIG. 15A. For the tests with different m.sub.2 in Group II, .sub.ROB,II and .sub.,II were 0.3773 Nm and 2.1036 Nm, respectively, during the forward bending process, and .sub.ROB,II and .sub.,II were 0.1789 Nm and 1.0981 Nm, respectively, during the backward bending process, as shown in FIG. 15B. The small values of the means and SDs in the two groups indicate that .sub.ROB is not affected by {dot over ()} and m.sub.2.

[0099] For the tests with different .sub.cam,ini in Group III, .sub.ROB,err,m (m=5, 6, 7) changes significantly, as shown in FIG. 15C. From (13) and (14), .sub.cam and .sub.VSMOD (.sub.cam) are changed by .sub.cam,ini at a given trunk angle , which indicates that changes of relative positions of components in the ROBUTS and the transmitted torque, respectively, can be possible reasons that .sub.ROB is related to .sub.cam,ini. To study the influence of the relative angles, curves between .sub.ROB,err,m and .sub.cam are plotted at different .sub.cam,ini (FIG. 15D, and results show that the ROBUTS output torque does not change with .sub.cam,ini when .sub.VSMOD(.sub.cam) is the same. Thus, the transmitted torque but not relative positions is the main reason, and the error _(ROB,err) is positively related to _VSMOD (_cam), as shown by the three points in A, B and C in FIG. 15C.

Modified Mechanic Model of the ROBUTS

[0100] Based on the fact that there is a positive correlation between .sub.ROB,err and .sub.VSMOD(.sub.cam), the mechanism of the error comes from the friction caused by the transmitted torque, and a modified mechanic model {circumflex over ()}.sub.ROB,mod is proposed here to replace the original model .sub.ROB,mod. Since .sub.ROB=.sub.4f.sub.4() from (5) and the accuracy of the kinematic relationship f.sub.4() has been proved, a modified PEA output torque model {circumflex over ()}.sub.4,mod is developed here to obtain modified model {circumflex over ()}.sub.ROB,mod={circumflex over ()}.sub.4,modf.sub.4():

[00025]$\begin{array}{cc}{\widehat{}}_{4,\mathrm{mod}}={}_{4,\mathrm{mod}}+{\widehat{}}_{4,\mathrm{err}}& \left(30\right)\end{array}$

where .sub.4,mod is the original model and {circumflex over ()}.sub.4,err is the error model to modify the PEA output torque, which can be the friction torque in the planetary gear set.

[0101] As shown in FIGS. 16A-16C, (a) a free-body diagram of the planet gear, where O.sub.s is the center of the sun gear (as well as OLINK), P.sub.1 and C.sub.1 are the pitch point and contact point (approaching P.sub.1) between the sun gear and planet gear, respectively, P.sub.2 and C.sub.2 are the pitch point and contact point (approaching P.sub.2) between the ring gear and planet gear, respectively, N.sub.1(N.sub.2) and f.sub.1(f.sub.2) are the normal and friction forces applied on the planet gear by the sun (ring) gear, respectively, r.sub.sun,b and r.sub.ring,b are the base circle radius of the sun gear and ring gear, respectively, and l.sub.1 and l.sub.2 are the moment arms of f.sub.1 and f.sub.2, respectively. Variables with the prime are those during recession processes of the contact point C.sub.k(k=1,2) to the pitch point P.sub.k. (b) The free-body diagram of the sun gear, where .sub.VSMOD is the transferred torque from the VSMOD. (c) The free-body diagram of the ring gear, where .sub.ring is the transferred torque from the SCMOD.

[0102] Assuming that the ROBUTS works in quasi-steady states, a free-body diagram of the planet gear of the planetary gear set is shown in FIG. 16A. The moments applied on a planet gear include the torque from the OLINK, which is the reaction of the PEA output torque {circumflex over ()}.sub.4,mod, the torques of the normal force N.sub.1 and friction f.sub.1 that come from the sun gear, whose moment arms are the sun gear's base circle radius r.sub.sun,b and a time-variant length l.sub.1, respectively, and the torques of the normal force N.sub.2 and friction f.sub.2 that come from the ring gear, whose moment arms are the ring gear's base circle radius r.sub.ring,b and a time-variant length l.sub.2, respectively. Thus, the moment balance equation of the planet gear is

[00026]$\begin{array}{cc}{N}_2{r}_{\mathrm{sun},b}+f_I{l}_1+N_2{r}_{\mathrm{ring},b}-f_2{l}_2-{\widehat{}}_{4,\mathrm{mod}}=0& \left(31\right)\end{array}$

[0103] In the original model of t.sub.4,mod developed in Section III, no frictions f.sub.1 and f.sub.2 are considered and its balance equation is N.sub.1r.sub.sun,b+N.sub.2r.sub.ring,b.sub.4,mod=0. Thus, the difference that comes from the frictions is the error model in (30):

[00027]$\begin{array}{cc}{\widehat{}}_{4,\mathrm{err}}=f_1{l}_1-f_2{l}_2& \left(32\right)\end{array}$

[0104] Based on the Coulomb friction model, frictions are f.sub.1=N.sub.1 and f.sub.2=N.sub.2, where =0.3 is the friction coefficient between the steel teeth. Since contact points between meshed gears are on the lines of action, the moment arms l.sub.1 and l.sub.2 are positively related to the base circle radii r.sub.sun,b and r.sub.ring,b, respectively, as shown in FIG. 16A. Meanwhile, l.sub.1 and l.sub.2 change periodically with the contact points that move on the lines of action. Taking the two factors into consideration, simplified models of the moment arms are l.sub.1=y.sub.1r.sub.sun,b and l.sub.2=y.sub.2r.sub.ring,b, where periodic coefficient functions y.sub.k(k=1,2) are

[00028]$\begin{array}{cc}{y}_k=a_k+b_k\cos \left({}_k{}_{\mathrm{cam}}+{}_k\right)\left(k=1,2\right)& \left(33\right)\end{array}$

where constants a.sub.k and b.sub.k represent the mean and magnitude of {circumflex over ()}.sub.4,err, respectively, and angular frequency .sub.k and phase angle .sub.k describe the periodicity and shape of {circumflex over ()}.sub.4,err, respectively. To obtain the relationship between the normal forces and the VSMOD output torque, the moment balance equations of the sun and ring gears are used (FIGS. 16B and 16C):

[00029]$\begin{array}{cc}{}_{\mathrm{VSMOD}}-N_1{r}_{\mathrm{sun},b}-f_1{l}_1=0& \left(34\right)\end{array}$$\begin{array}{cc}{}_{\mathrm{ring}}-N_2{r}_{\mathrm{ring},b}+f_2{l}_2=0& \left(35\right)\end{array}$

where .sub.ring is the torque on the ring gear, and .sub.ring=(N.sub.ring/N.sub.sun). .sub.VSMOD when inertial forces of gears are neglected. Substituting the friction model into (34) and (35) yields N.sub.1=.sub.VSMOD/[(1+y.sub.1)r.sub.sun,b] and N.sub.2=N.sub.ring.sub.VSMOD/[N.sub.sun(1+y.sub.2)r.sub.ring,b], and substituting the resultant normal forces into (32) yields the error model of the PEA output torque

[00030]$\begin{array}{cc}{\widehat{}}_{4,\mathrm{err}}=\left(-\frac{y_1}{1-y_1}+\frac{y_2}{1+y_2}\frac{N_{\mathrm{ring}}}{N_{\mathrm{sun}}}\right){}_{\mathrm{VSMOD}}& \left(36\right)\end{array}$

Substituting (36) into (30) yields the model of {circumflex over ()}.sub.4,mod, so that the modified model of the ROBUTS support torque can be obtained by {circumflex over ()}.sub.ROB,mod={circumflex over ()}.sub.4,modf.sub.4().

[0105] Parameter identification and evaluation of the modified ROBUTS support torque model

[0106] In the {circumflex over ()}.sub.ROB,mod, parameters of coefficient functions y.sub.k(k=1,2) are underdetermined. Since the torque errors .sub.ROB,err were different in the forward and backward bending processes, as shown in FIGS. 15A-15D, the coefficient functions are classified as y.sub.k.sup.f and y.sub.k.sup.b, where f and b represent the forward and backward bending processes, respectively. Two optimization problems are designed to calculate parameters a.sub.k.sup.f, b.sub.k.sup.f, .sub.k.sup.f, .sub.k.sup.f and a.sub.k.sup.b, b.sub.k.sup.b, .sub.k.sup.b, .sub.k.sup.b

[00031]$\begin{array}{cc}\underset{a_{k^{}}^f,b_k^f,{}_{k^{}}^f,{}_k^f}{\min }{.Math.{\widehat{}}_{4,\mathrm{err}}^f-{}_{\mathrm{ROB},\mathrm{err}}^f/f_4\left(\right).Math.}_2& \left(37\right)\end{array}$$\underset{a_k^b,b_k^b,{}_k^b,{}_k^b}{\min }{.Math.{\widehat{}}_{4,\mathrm{err}}^b-{}_{\mathrm{ROB},\mathrm{err}}^b/f_4\left(\right).Math.}_2$

where .Math..sub.2 represents the 2-norm, .sub.ROB,err.sup.f and .sub.ROB,err.sup.b are torque errors during the forward and backward bending processes, respectively, calculated by (23) with use of the original model, and {circumflex over ()}.sub.4,err.sup.f and {circumflex over ()}.sub.4,err.sup.b are calculated by the modified model in (36). Data of the two tests in Group II were used to identify the parameters by solving (37), which yields

[00032]$\begin{array}{cc}\{\begin{array}{c}{y}_1^f=0.00+1.12\cos \left(35{}_{\mathrm{cam}}-\right)\\ y_2^f=-0.11-0.01\cos \left(35{}_{\mathrm{cam}}+\frac{}{12}\right)\\ y_1^b=1.87+0.16\cos \left(35{}_{\mathrm{cam}}+\frac{}{3}\right)\\ y_2^b=-0.12-0.10\cos \left(35{}_{\mathrm{cam}}-\frac{2}{3}\right)\end{array}& \left(38\right)\end{array}$

[0107] The identified angular frequency .sub.k=35 is equal to N.sub.ringN.sub.sun/(N.sub.ring+N.sub.sun), and the reason is illustrated here. The angular velocity of the sun gear relative to that of the carrier is .sub.camN.sub.ring/(N.sub.ring+N.sub.sun) when the motor does not move, which can be calculated with use of (11). Thus, the sun rotates N.sub.ring/(N.sub.ring+N.sub.sun) revolutions relative to the carrier when the cam rotates one revolution, and the meshing frequency of the teeth between the sun and planet gears is N.sub.ringN.sub.sun/(N.sub.ring+N.sub.sun) since there are N.sub.sun teeth per revolution of the sun gear, which yields the frequency of y.sub.k(k=1,2). With the identified coefficient functions y.sub.k.sup.f and y.sub.k.sup.b, the modified model {circumflex over ()}.sub.ROB,mod torque can be obtained.

[0108] Data from Section IV.B are used to evaluate the accuracy of the identified model {circumflex over ()}.sub.ROB,mod, which are (a) controlled experimental condition with {dot over ()}=0.6 Deg/s, m.sub.2=15 kg, .sub.cam,ini=0 Deg (m=1), (b) fast trunk angular velocity condition with {dot over ()}=0.9 Deg/s (m=2), (c) small trunk mass condition with m.sub.2=12 kg (m=4), (d) medium initial cam angle condition with .sub.cam,ini=20 Deg (m=6), and (e) large initial cam angle condition with .sub.cam,ini=40 Deg (m=7). The ROBUTS support torque error of the modified model is {circumflex over ()}.sub.ROB,err={circumflex over ()}.sub.4,errf.sub.4().

[0109] Results of {circumflex over ()}.sub.ROB,err and .sub.ROB,err are shown in FIGS. 17A-17F including a comparison of ROBUTS support torque errors using original and modified ROBUTS output torque models under different experimental conditions: (a) m=1 ({dot over ()}=0.6 Deg/s, m.sub.2=15 kg, .sub.cam,ini=0 Deg), (b) m=2 ({dot over ()}=0.9 Deg/s), (c) m=4 (m.sub.2=12 kg), (d) m=6 (.sub.cam,ini=20 Deg), and (e) m=7 (.sub.cam,ini=40 Deg), (f) ROBUTS support torque evaluation results. Reference, Modified and Original represent support torques from the reference .sub.ref.sup.(i), the modified model {circumflex over ()}.sub.ROB.sup.(i) and the original model .sub.ROB.sup.(i), with i=1, 2, . . . , 7. The mean of the error between the experimental data and the modified model {circumflex over ()}.sub.ROB,mod, {circumflex over ()}.sub.ROB,err=1/n .sub.i=1.sup.n {circumflex over ()}.sub.ROB,err(.sub.i), and that of the original model .sub.ROB,mod, .sub.ROB,err=1/n .sub.i=1.sup.n .sub.ROB,err(.sub.i), are shown in Table II. The errors of the modified model are all smaller, which shows that the modified model significantly improved the prediction accuracy of the ROBUTS support torque.

TABLE-US-00002 TABLE II {circumflex over ()}.sub.ROB, err and .sub.ROB, err Under Different Experimental Conditions Experimental conditions Bending directions Condi- Forward Backward Groups tions {circumflex over ()}.sub.ROB, err/ {circumflex over ()}.sub.ROB, err/ (M) (m) Nm .sub.ROB, err/Nm Nm .sub.ROB, err/Nm I 1* 0.6817 0.5942 0.2080 6.0443 2 1.1751 0.0756 0.6683 6.1607 II 4 0.5639 0.7255 0.1654 5.9617 III 6 0.4197 0.9993 0.1589 3.5982 7 0.1580 1.3472 0.4807 1.7466 Note: The experimental condition with * was the controlled condition.

[0110] Finally, the control accuracy of the ROBUTS support torque at fixed trunk angles were evaluated. Seven different trunk angles .sup.(i), i=1, 2, . . . , 7 were chosen with .sub.ref.sup.(i)=m.sub.2g cos .sup.(i) as the reference support torques to be achieved. Motor angles {circumflex over ()}.sub.motor.sup.(i) and .sub.motor.sup.(i) that are calculated from the modified and original models, respectively, are used to control the ROBUTS to provide the reference torques. The real ROBUTS support torques {circumflex over ()}.sub.ROB.sup.(i) and .sub.ROB.sup.(i) that are measured at {circumflex over ()}.sub.motor.sup.(i) and .sub.motor.sup.(i), respectively, are shown in FIG. 17F. The mean and SD of the difference between {circumflex over ()}.sub.ROB.sup.(i) (controlled by the modified model) and .sub.ref.sup.(i) are 0.2057 Nm and 0.3064 Nm, respectively, and those between .sub.ROB.sup.(i) (controlled by the original model) and .sub.ref.sup.(i) are 1.6502 Nm and 1.1858 Nm, respectively. Results show that accurate control of the ROBUTS support torque can be achieved by the modified model.

[0111] This work presents a robotic trunk training device ROBUTS for the assistance of upper-trunk stabilization training. The device is made up of a semi-active PEA that combines a passive VSMOD and an active SCMOD, and it is connected to the patient trunk via a CONMOD. The compliant and controllable support torque on the trunk can be achieved with use of the PEA, and joint misalignment between the robot and human joints can be avoided using the CONMOD. The kinematic models of the ROBUTS are validated using a prototype, and the mechanic model is modified by a friction model of the planetary gear set, where a mechanism of the friction torque is proposed to illustrate the torque differences when the trunk moves back and forth. Experimental results show that the output torque of the ROBUTS can be accurately controlled with use of the modified mechanic model. The development of the PEA-based robotic device and output torque control method is the foundation for developing an AAN-based force-adaptive controller for the ROBUTS, which can be used in the muscle strength evaluation and impedance control of the trunk movement.

[0112] For purposes of this description, certain advantages and novel features of the aspects and configurations of this disclosure are described herein. The described methods, systems, and apparatus should not be construed as limiting in any way. Instead, the present disclosure is directed toward all novel and nonobvious features and aspects of the various disclosed aspects, alone and in various combinations and sub-combinations with one another. The disclosed methods, systems, and apparatus are not limited to any specific aspect, feature, or combination thereof, nor do the disclosed methods, systems, and apparatus require that any one or more specific advantages be present or problems be solved.

[0113] Although the figures and description may illustrate a specific order of method steps, the order of such steps may differ from what is depicted and described, unless specified differently above. Also, two or more steps may be performed concurrently or with partial concurrence, unless specified differently above. Such variation may depend, for example, on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations of the described methods could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps, and decision steps.

[0114] Features disclosed in this specification (including any accompanying claims, abstract, and drawings), and/or all of the steps of any method or process so disclosed, may be combined in any combination, except combinations where at least some of such features and/or steps are mutually exclusive. The claimed features extend to any novel one, or any novel combination, of the features disclosed in this specification (including any accompanying claims, abstract, and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

[0115] As used in the specification and the appended claims, the singular forms a, an, and the include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from about one particular value, and/or to about another particular value. When such a range is expressed, another aspect includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent about, it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. The terms about and approximately are defined as being close to as understood by one of ordinary skill in the art. In one non-limiting aspect the terms are defined to be within 10%. In another non-limiting aspect, the terms are defined to be within 5%. In still another non-limiting aspect, the terms are defined to be within 1%.

[0116] The terms coupled, connected, and the like as used herein mean the joining of two members directly or indirectly to one another. Such joining may be stationary (e.g., permanent) or moveable (e.g., removable or releasable). Such joining may be achieved with the two members or the two members and any additional intermediate members being integrally formed as a single unitary body with one another or with the two members or the two members and any additional intermediate members being attached to one another. If coupled or variations thereof are modified by an additional term (e.g., directly coupled), the generic definition of coupled provided above is modified by the plain language meaning of the additional term (e.g., directly coupled means the joining of two members without any separate intervening member), resulting in a narrower definition than the generic definition of coupled provided above. Such coupling may be mechanical, electrical, or fluidic. For example, circuit A communicably coupled to circuit B may signify that the circuit A communicates directly with circuit B (i.e., no intermediary) or communicates indirectly with circuit B (e.g., through one or more intermediaries).

[0117] Certain terminology is used in the following description for convenience only and is not limiting. The words right, left, lower, and upper designate direction in the drawings to which reference is made. The words inner and outer refer to directions toward and away from, respectively, the geometric center of the described feature or device. The words distal and proximal refer to directions taken in context of the item described and, with regard to the instruments herein described, are typically based on the perspective of the practitioner using such instrument, with proximal indicating a position closer to the practitioner and distal indicating a position further from the practitioner. The terminology includes the above-listed words, derivatives thereof, and words of similar import.

[0118] Throughout the description and claims of this specification, the word comprise and variations of the word, such as comprising and comprises, means including but not limited to, and is not intended to exclude, for example, other additives, components, integers or steps. Exemplary means an example of and is not intended to convey an indication of a preferred or ideal aspect. Such as is not used in a restrictive sense, but for explanatory purposes.

[0119] The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention.