MOTION PLATFORM

Abstract

The present invention relates to a motion platform that moves in two degrees of rotational freedom that can be used to simulate board activities such as skateboarding and surfing and is readily extended to simulate other experiences such as skiing, driving, flying, and even boxing, through the attachment of the appropriate apparatus. The motion platform comprises a pivotable table attached to a base with two toothed belts attached at quadrants of the table, with the belts attached to a pair of ball-screws mounted orthogonally in the base. Pulleys mounted in the quadrants of the base redirect the belts so that they travel parallel to the ball screws. Cams maintain proper tension in the belts as the table pivots. The motion platform includes a programmable controller that can drive the table in terms of position but can also drive the platform according to a mathematical model where the physical table is attached to a virtual table through virtual springs with dynamic virtual spring rates and virtual dampers with dynamic virtual coefficients of damping. Here, position commands are applied not to the physical table but to the virtual table with the final position of the physical table determined through the solution of spring-mass-damper equations of motion using the dynamic spring rates, dynamic coefficients of damping, measured torque on the table, and where the mass corresponds to virtual moments of inertia of a simulated board such as a paddle board with the moment of inertia of the physical table and connected moving parts factored out; the mathematical model able to simulate a variety of environments such as a paddle board on water with waves, a snowboard on fresh powder, or even quicksand.

Claims

1. A motion platform, comprising: a table rotatably mounted to a base via a joint means; a belt means with each distal end attached to said table at points straddling said joint means; a linear-actuator means attached to said base with said linear-actuator means having a driveable element that is attached to said belt means such that translation of said driveable element tensions said belt means, which in turn pivots said table about said joint means; at least one pulley means attached to said base that redirects said belt means such that said belt means travels substantially parallel to said linear-actuator means; a tensioning means attached to said base that takes up or gives slack in said belt means that occurs as a result of geometry changes as said table pivots.

2. A motion platform as in claim 1, wherein said belt means runs underneath said linear-actuator means, thereby minimizing the height of said motion platform for a given maximum deflection angle of said table.

3. A motion platform as in claim 1, wherein said belt means has teeth allowing for positive engagement with a toothed-pulley means.

4. A motion platform as in claim 3, wherein said tensioning means comprises a cam affixed to a toothed-pulley means that engages said belt means, said toothed-pulley means rotatably mounted to a cam carriage that is rotatably or slidably mounted to said base, with said cam contacting a roller that is rotatably mounted to said base, whereby translation of said belt means causes said toothed-pulley means to rotate in congruence with said cam, with said cam urging said cam carriage to move a distance necessary to take up or give slack to said belt means as needed to prevent over-tension or under-tension of said belt means as said table pivots through its range of travel.

5. A motion platform as in claim 4, wherein said cam can be rotatably adjusted and fixed at a certain angle with respect to said toothed-pulley means to adjust and set timing between said cam and said belt means.

6. A motion platform as in claim 4, wherein said tensioning means further comprises a roller carriage upon which said roller is rotatably mounted, with said roller carriage being rotatably or slidably mounted to said base, and with said roller carriage including an adjustment means allowing said roller to be moved and fixed with respect to said to base to thereby remove backlash in or pre-tension said belt means.

7. A motion platform as in claim 6, wherein said tensioning means further comprises a spring that urges said cam carriage against said belt means to establish pre-tension in said belt means.

8. A motion platform as in claim 1, wherein said linear-actuator means is comprised of a servo driving a ball screw, and wherein said driveable element is a ball-screw nut rotatably and translatably attached to said ball screw and slidably attached to said base.

9. A motion platform, comprising: a table rotatably mounted to a base via a joint means that allows two degrees of rotational freedom; a belt means X with each distal end attached to said table at points X straddling said joint means; a linear-actuator means X attached to said base with said linear-actuator means having a driveable element X that is attached to said belt means X such that translation of said driveable element X tensions said belt means X, which in turn pivots said table in a plane X; at least one pulley means X attached to said base that redirects said belt means X such that said belt means X travels substantially parallel to said linear-actuator means; a tensioning means X to take up or give slack in said belt means X as a result of geometry changes as said table pivots in said plane X; a belt means Y with each distal end attached to said table at points Y straddling said joint means, said points Y being substantially orthogonal to said points X; a linear-actuator Y attached to said base with said linear-actuator means having a driveable element Y that is attached to said belt means Y such that translation of said driveable element Y tensions said belt means Y, which in turn pivots said table in a plane Y substantially orthogonal to said plane X; at least one pulley means Y attached attached to said base that redirects said belt means Y such that said belt means Y travels substantially parallel to said linear-actuator means Y; a tensioning means Y to take up or give slack in said belt means Y that occur as a result of geometry changes as said table pivots in said plane Y.

10. A motion platform as in claim 9, wherein said belt means X at each distal end is attached to said table via a belt-joint means X that allows for two degrees of rotational freedom, wherein the center of rotation of said belt-joint means X is collinear with the center of rotation of said joint means; and wherein said belt means Y at each distal end is attached to said table via a belt-joint means Y that allows for two degrees of rotational freedom, wherein the center of rotation of said belt-joint means Y is collinear with the center of rotation of said joint means.

11. A motion platform as in claim 9, wherein said linear-actuator means Y is fixed in said plane Y at an angle with respect to said base such that said belt means Y travels over said linear-actuator means X, thereby increasing the travel length of said linear-actuator means X and Y ultimately the deflection of said table for a given footprint and height of said motion platform.

12. A motion platform as in claim 9, wherein said belt means X runs underneath said linear-actuator means X and wherein said belt means Y runs underneath said linear-actuator means Y, thereby minimizing the height of said motion platform for a given maximum deflection angle of said table.

13. A motion platform as in claim 9, wherein said belt means X and said belt means Y have teeth allowing for positive engagement with a toothed-pulley means.

14. A motion platform as in claim 9, wherein said tensioning means X comprises a cam X affixed to a toothed-pulley means X that engages said belt means X, said toothed-pulley means X rotatably mounted to a cam carriage X that is rotatably or slidably mounted to said base, with said cam X contacting a roller X that is rotatably mounted to said base, whereby translation of said belt means X causes said toothed-pulley means X to rotate in congruence with said cam X, with said cam X urging said cam carriage X to move a distance necessary to take up or give slack to said belt means X as needed to prevent over-tension or under-tension of said belt means X as said table pivots through its range of travel in said plane X; and wherein said tensioning means Y comprises a cam Y affixed to a toothed-pulley means Y that engages said belt means Y, said toothed-pulley means Y rotatably mounted to a cam carriage Y that is rotatably or slidably mounted to said base, with said cam Y contacting a roller Y that is rotatably mounted to said base, whereby translation of said belt means Y causes said toothed-pulley means Y to rotate in congruence with said cam Y, with said cam Y urging said cam carriage Y to move a distance necessary to take up or give slack to said belt means Y as needed to prevent over-tension or under-tension of said belt means Y as said table pivots through its range of travel in said plane Y.

15. A motion platform as in claim 14, wherein said cam X can be rotatably adjusted and fixed at a certain angle with respect to said toothed-pulley means X to adjust and set timing between said cam X and said belt means X; and wherein said cam Y can be rotatably adjusted and fixed at a certain angle with respect to said toothed-pulley means Y to adjust and set timing between said cam Y and said belt means Y.

16. A motion platform as in claim 14, wherein said tensioning means X further comprises a roller carriage X upon which said roller X is rotatably mounted, with said roller carriage X being rotatably or slidably mounted to said base, and with said roller carriage X including an adjustment means X allowing said roller X to be moved and fixed with respect to said to base to thereby remove backlash in or pre-tension said belt means X; and wherein said tensioning means Y further comprises a roller carriage Y upon which said roller Y is rotatably mounted, with said roller carriage Y being rotatably or slidably mounted to said base, and with said roller carriage Y including an adjustment means Y allowing said roller Y to be moved and fixed with respect to said to base to thereby remove backlash in or pre-tension said belt means Y.

17. A motion platform as in claim 14, wherein said tensioning means X further comprises a spring X that urges said cam carriage X against said belt means X to establish pre-tension in said belt means X; and wherein said tensioning means Y further comprises a spring Y that urges said cam carriage Y against said belt means Y to establish pre-tension in said belt means Y.

18. A motion platform as in claim 14, wherein said linear-actuator means X is comprised of a servo X driving a ball screw X, and wherein said driveable element X is a ball-screw nut X rotatably and translatably attached to said ball screw X and slidably attached to said base; and wherein said linear-actuator means Y is comprised of a servo Y driving a ball screw Y, and wherein said driveable element Y is a ball-screw nut Y rotatably and translatably attached to said ball screw Y and slidably attached to said base.

19. A motion platform, comprising: a table that can move in at least one and up to six degrees of freedom; at least one actuator means connecting said table to a base; a force-measuring means than can measure external forces or external torques or both external forces and external torques on said table, wherein said force-measuring means may include said actuator means; a programmable-controller means that can drive said actuator means according to a mathematical model comprising a virtual table that can virtually move in at least one and up to six degrees of freedom, said virtual table connected virtually to said table through at least one virtual spring that has a virtual spring rate that is programmable and dynamic and at least one virtual damper with a virtual damping coefficient that is programmable and dynamic; wherein movement commands may be applied to said virtual table with the resulting movement of said table being determined by solving equations of motion for a virtual spring-mass-damper system using said virtual spring rate or rates, said virtual damping coefficient or coefficients, measured external forces or external torques or both external forces and external torques as determined by said force-measuring means, and wherein said mass in said spring-mass-damper system may correspond to virtual moments of inertia of a simulated object such as a virtual surfboard with the moments of inertia of said table and said actuator means factored out.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0032] For a more complete understanding of the invention, reference is made to the following description and accompanying drawings, in which:

[0033] FIG. 1 is a top view in perspective of a motion platform;

[0034] FIG. 2 is a bottom view in perspective of a motion platform;

[0035] FIG. 3 is a view in section of a motion platform in plane XZ;

[0036] FIG. 4 is a view in section of a motion platform in plane YZ;

[0037] FIG. 5 is a view in section of a motion platform in plane YZ;

[0038] FIG. 6 is a view of a mathematical model for a motion-platform controller;

[0039] FIG. 7 is a view of a mathematical model for a motion-platform controller; and

[0040] FIG. 8 is a graph showing the mechanical responsiveness of a motion-platform.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0041] Referring to FIGS. 1-5, a motion platform 1 has a table 2 that pivots in two degrees of rotational freedom, providing for the simulation of board sports such as skateboarding, surfing, and snowboarding, and other activities and exercise routines yet to be invented that entail balance, agility, and footwork. Further, the platform is extensible where an additional apparatus such as a racing rig or skiing rig may be attached and integrated with the platform controller. Motion platform 1, which is not limited to motion simulation, can handle high-torque loads and is capable of large deflection angles in backlash-free, precise motion.

[0042] Table 2 is attached to a post 3 via a joint 4 that provides two degrees of rotational freedom, which in the preferred embodiment is a universal joint. Post 3 is attached to a base 5, which is comprised of a base arm 6 and a base arm 7, mounted orthogonally to each other, base arm 6 and post 3 defining a plane XZ, and base arm 7 and post 3 defining a plane YZ, plane YZ being orthogonal to plane XZ. FIGS. 4 and 5 show base arm 7 in section bridging base arm 6 via a miter joint 8.

[0043] FIG. 3 shows base arm 6 in section, which is comprised of a square tube 9, within which are mounted a belt-tensioning assembly 11 and a ball-screw assembly 10. FIGS. 4 and 5 show base arm 7 in section, which is comprised of a square tube 12, within which are mounted a belt-tensioning assembly 14 and a ball-screw assembly 13.

[0044] As shown in FIG. 3, attached to table 2 at opposite edges, is a toothed belt 15 via a tie-rod end 16 and a tie-rod end 17 that each allow two degrees of rotational freedom. Critically, the centers of rotation of tie-rod ends 16 and 17 are collinear with the center of rotation of joint 4 and coplanar with plane XZ. Toothed belt 15 is attached to tie-rod ends 16 and 17 via a belt clamp 18 and a belt clamp 19. Looking from left to right, toothed belt 15 runs down from belt clamp 18, through belt-tensioning assembly 11, through ball-screw assembly 10, and up to belt clamp 19.

[0045] In FIG. 3, more specifically, toothed belt 15 runs underneath a smooth pulley 20, over a cam assembly 21, and under a smooth pulley 22, with smooth pulleys 20 and 22 rotatably mounted to belt-tensioning assembly 11. Cam assembly 21 is comprised of a pair of cam plates 23 that sandwich a toothed pulley 24 with an array of cam bolts 25 clamping cam assembly 21 together. Toothed belt 15 engages toothed pulley 24 allowing translation of toothed belt 15 to urge rotation of cam assembly 21. The primary reason that teeth are needed in toothed belt 15 is to drive cam assembly 21.

[0046] Cam assembly 21 is rotatably attached to a swing arm 26 via a pair of cam bearings 27, with swing arm 26 rotatably attached to belt-tensioning assembly 11. Cam plates 23 ride on a roller 28 that is rotatably mounted in a roller carriage 29, which is slidably mounted in belt-tensioning assembly 11. Roller carriage 29 may be advanced upward relative to belt-tensioning assembly 11 via a set of set screws 30, thereby causing roller 28 to urge cam assembly 21 up against toothed belt 15, adding pretension thereto. A spring (not shown) may be added as well to further urge cam assembly 21 upward, although table 2 and toothed belt 15 have a certain stiffness whereby a minimal deflection thereof can add tension to toothed belt 15 with fine-tuning possible via set screws 30.

[0047] Coming out of belt-tensioning assembly 11, toothed belt 15 runs underneath a ball screw 31 and a smooth pulley 52, both rotatably attached to ball-screw assembly 10. Toothed belt 15 is attached to a ball nut 32 via a belt clamp 33 where rotation of ball screw 31 causes ball nut 32 to translate, in turn, causing toothed belt 15 to translate, which in turn causes table 2 to pivot in plane XZ. Ball nut 32 rides on a pair of linear-guide rails 51, shown in section in FIG. 4, that stabilize and prevent the rotation of ball nut 32 as it translates along ball screw 31.

[0048] As table 2 pivots counter-clockwise from horizontal, the length of belt between tie-rod end 17 and smooth pulley 52 grows faster than the rate at which the length between tie-rod end 16 and smooth pulley 20 shrinks, necessitating that slack be added to toothed belt 15 at a rate governed by the change in perimeter. Conversely, as table 2 pivots back clockwise, slack needs to be removed. This is the purpose of belt-tensioning assembly 11, whereby the pivoting of cam assembly 21 on swing arm 26 adds or removes slack as needed in toothed belt 15 to maintain roughly constant tension therein as table 2 pivots through its range. The pivot angle of swing arm 26 is governed by the geometry of cam plates 23 in contact with roller 28 where necessary changes in contact radius are timed with translation of toothed belt 15.

[0049] Because the timing between cam plates 23 and toothed belt 15 is critical, the angle between cam plates 23 and toothed pulley 24 may be fine-tuned to advance or retard timing between the two. Toothed pulley 24 has an array of oversized holes 53 through which cam bolts 25 pass that allow cam plates 23 to be rotated relative to toothed pulley 24 a small angle and fixed at that angle by tightening cam bolts 25. Both toothed pulley 24 and cam plates 23 are mounted on cam bearings 27 allowing the two to rotate about a common axis.

[0050] Referring to FIG. 2, driving ball screw 31 is a servo 34 via a belt drive 35 with servo 34 rotatably mounted to base arm 6 via a hinge 36 with tension in belt drive 35 adjusted via a tensioning screw 37. Similarly, in FIG. 1, a servo 38 drives a ball screw 39, which is rotatably mounted in ball-screw assembly 13 as shown in FIGS. 4 and 5. Driving servos 34 and 38 and coordinating motion there between is a programmable controller (not shown). The motion of table 2 is substantially free from backlash by virtue of ball-screw mechanism, in general, having negligible backlash and the final connection to servo 34, made via belt drive 35, also having negligible backlash.

[0051] FIGS. 4 and 5 show a toothed belt 40, which, looking from left to right, runs from a tie-rod end 41, down through belt-tensioning assembly 14 and ball-screw assembly 13, and up to a tie-rod end 42, with tie-rod ends 41 and 42 being attached to table 2 on edges orthogonal to tie-rod ends 16 and 17. As is the case with the XZ plane, the centers of rotation of tie-rod ends 41 and 42 are collinear with the center of rotation of joint 4 and coplanar with plane YZ. FIG. 5 shows table 2 at full deflection—18.5 degrees. Notice ball nut 54 is at its end of travel on ball screw 39.

[0052] Ball-screw assembly 13 is identical to ball-screw assembly 10. Belt-tensioning assembly 14 is nearly identical to belt-tensioning assembly 11 with the only difference being the inclusion of a toothed pulley 43, which is needed to redirect toothed belt 40 over miter joint 8. Toothed pulley 43 only requires teeth because it engages the tooth side of toothed belt 40. Functionally, the cam-tensioning and ball-screw mechanisms work identically in both base arms 6 and 7.

[0053] Miter joint 8 in base arm 7 allows the length of ball-screw assemblies 10 and 13 to be maximized for a given motion platform 1 footprint. Running toothed belts 15 and 40 underneath ball screws 31 and 39 minimizes the height of post 3 for a given maximum table 2 deflection angle.

[0054] FIGS. 6 and 7 show a mathematical model 44 for motion in the XZ and YZ planes that may be run by the programmable controller to drive table 2 deflection to simulate fluid environments such as a rider on a paddle board on water (not shown). In this model, table 2 and a virtual table 45 are both rotatably connected to a virtual base 46 and connected to each other via a virtual spring 47 with a dynamic virtual spring rate and a virtual damper 48 with a dynamic virtual coefficient of damping. Here, “dynamic” refers to a variable set via equation or lookup table or the like wherein, as the mathematical model is executing, the values may change.

[0055] Note that in FIGS. 6 and 7, virtual spring 47 and virtual damper 48 are purely illustrative. Mathematically, virtual spring 47 is a torsion spring and virtual damper 48 is a torsion damper with the center of pivot of virtual table 45 being concentric with joint 4. Also, in mathematical model 44, virtual spring 47 resists both clockwise and counter-clockwise rotation from horizontal.

[0056] The deflection of table 2 is determined by solving the equations of motion for a rotational spring-mass-damper system comprised of virtual spring 47 and virtual damper 48, where the applied torque on the system is the measured external torque applied to table 2 shown in FIG. 7 as torque T, and where the mass is the moment of inertia of a board or craft (not shown) with the actual moment of inertia of table 2 and connected moving parts factored out. The board or craft may be a physical object, or a portion thereof, attached to table 2 or a virtual object, in which case the moment of inertia would also be virtual. FIGS. 6 and 7 show motion in the XZ plane. Motion in the YZ plane is governed by its own rotational spring-mass-damper system with its own spring, damping, and inertia parameters.

[0057] In the XZ plane, torque T acting upon table 2 is sensed by servo 34 in concert with the programmable controller. To derive torque T accurately when table 2 is either accelerating or decelerating, its moment of inertia and that of the connected moving parts must be accounted for. Keeping table 2's moment as low as possible facilitates this derivation. Further, a drive mechanism between table 2 and servo 34 that allows torque to be transferred thereto without significant friction losses is also critical to accurately sensing torque T. Ball screws with lead angles over 5 degrees, as would be specified in the preferred embodiment, typically offer efficiencies over 95% for both forward and reverse operation, the latter where linear force on the ball nut imparts a torque to the ball screw. With toothed-belt drives having efficiencies of 98%, the overall table 2 to servo 34 efficiency ranges between 91-93%.

[0058] FIG. 7 shows a snapshot of table 2 in motion with applied torque T with the programmable controller running mathematical model 44. Here, virtual table 45 has been deflected to an angle θ.sub.v, and through the solution of the spring-mass-damper equations of motion, table 2 deflects to θ, which is about double θ.sub.v. Comparing FIG. 7 with FIG. 6, virtual spring 47 with a positive, less-than-infinite spring rate has been compressed a certain amount. If the spring rate were infinite, virtual spring 47 would essentially function as an inflexible rod causing the deflection of table 2 to exactly track the deflection of virtual table 45. Alternatively, if virtual damper 48 were infinitely stiff, the same result would apply—table 2 would exactly track virtual table 45 in deflection.

[0059] FIG. 7 could represent a variety of simulations. Applied torque T, for example, could represent a rider on a virtual paddle board shifting his weight to the left with a wave represented by virtual table 45 traveling left to right, which is now cresting on the right side of the board. As the wave continues its travel, virtual table 45 levels out, compressing virtual spring 47, urging table 2 clockwise against torque T. In this scenario, the coefficient of damping of virtual damper 48 would be set to a value that would cause table 2 to oscillate to mimic the bobbing of an actual paddle board, eventually settling down to a deflection angle θ where the simulated buoyancy of the virtual paddle board is in balance with torque T.

[0060] FIG. 8 is a graph that shows the responsiveness of table 2 at various deflection angles. Specifically, a plot 49 shows the incremental change in table 2 angle dθ with respect to the incremental translation dL of toothed belt 15 from table 2 deflection angle −17 degrees to +17 degrees. Ideally, plot 49 should be flat, which would indicate that the amount of incremental servo 34 rotation needed for a given incremental table 2 deflection would remain constant regardless of table 2 angle. As shown, plot 49 approaches the ideal.

[0061] In contrast, a plot 50 in FIG. 8 shows the responsiveness of a gearmotor-based motion platform (not shown) where a pitman-arm travel of −90 degrees to +90 degrees translates to a table deflection of −10 degrees to +10 degrees. At the extremes, responsiveness goes to 0 where incremental rotation of the servo driving the gearmotor yields nearly zero incremental table deflection. Also, note that when the pitman arms are at the extremes of −90 degrees or +90 degrees, no torque on the table can be transmitted back to the servo. As discussed above, for a given table-deflection range, pitman-arm travel can be reduced to stay out of the low-responsiveness bands if the pitman arm is made longer or the attachment point to the table is brought closer to the pivot point, or both, but this will increase the torque demand on the gearmotor.

[0062] It may thus be seen that the objects set forth above, among those made apparent from the preceding description, are efficiently attained and, because certain changes may be made in carrying out the above method and in the construction set forth without departing from the spirit and scope of the invention, it is intended that all matter contained in the above description and shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

[0063] It is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention herein described and all statements of the scope of the invention which, as a matter of language, might be said to fall there between.