SYSTEMS AND METHODS FOR HOSE ROUTING IN PROGRAMMABLE MOTION SYSTEMS

Abstract

A programmable motion robotic system is disclosed that includes a plurality of arm sections that are joined one to another at a plurality of joints to form an articulated arm; and a hose coupling an end effector of the programmable motion robotic system to a vacuum source, the hose being attached, in a joint portion of the hose, to at least two adjacent arm sections of the plurality of arm sections mutually attached to a joint of the plurality of joints such that the joint portion of the hose remains substantially outside of any plane defined by motion of the mutually adjacent arm sections when rotated about the joint.

Claims

1. A programmable motion robotic system comprising a plurality of arm sections that are joined one to another at a plurality of joints to form an articulated arm; and a hose coupling an end effector of the programmable motion robotic system to a vacuum source, said hose being attached, in a joint portion of the hose, to at least two adjacent arm sections of the plurality of arm sections mutually attached to a joint of the plurality of joints such that the joint portion of the hose remains substantially outside of any plane defined by motion of the mutually adjacent arm sections when rotated about the joint.

2. The programmable motion robotic system as claimed in claim 1, wherein the hose includes at least two joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose each remain substantially outside of any plane defined by motion of the mutually adjacent arm sections when rotated about the respective joint.

3. The programmable motion robotic system as claimed in claim 1, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a flow rate of at least 100 cubic feet per minute.

4. The programmable motion robotic system as claimed in claim 1, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a vacuum pressure of no more than 50,000 Pascals below atmospheric.

5. The programmable motion robotic system as claimed in claim 1, wherein the hose has an inner diameter of at least 1 inch.

6. The programmable motion robotic system as claimed in claim 1, wherein the hose has an inner diameter of at least 3 inches.

7. The programmable motion robotic system as claimed in claim 1, wherein the hose has a helical ribbing.

8. The programmable motion robotic system as claimed in claim 1, wherein the hose includes at least three joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose each remain substantially outside of any plane defined by motion of the mutually adjacent arm sections when rotated about the respective joint.

9. The programmable motion robotic system as claimed in claim 1, wherein the hose includes no portions of the hose that is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose each remain substantially inside of any plane defined by motion of the mutually adjacent arm sections when rotated about the respective joint.

10. The programmable motion robotic system as claimed in claim 1, wherein the end effector includes a flexible bellows.

11. A programmable motion robotic system comprising a plurality of arm sections that are joined one to another at a plurality of joints to form an articulated arm; and a hose coupling an end effector of the programmable motion robotic system to a vacuum source, said hose being attached, in a joint portion of the hose, to at least two adjacent arm sections of the plurality of arm sections mutually attached to a joint of the plurality of joints such that the joint portion of the hose defines a plane that includes a direction that is generally parallel with an axis of rotation of the joint.

12. The programmable motion robotic system as claimed in claim 11, wherein the hose includes at least two joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose each defines a plane that includes a respective direction that is generally parallel with an axis of rotation of the respective joint.

13. The programmable motion robotic system as claimed in claim 11, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a flow rate of at least 100 cubic feet per minute.

14. The programmable motion robotic system as claimed in claim 11, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a vacuum pressure of no more than 50,000 Pascals below atmospheric.

15. The programmable motion robotic system as claimed in claim 11, wherein the hose has an inner diameter of at least 1 inch.

16. The programmable motion robotic system as claimed in claim 11, wherein the hose has an inner diameter of at least 3 inches.

17. The programmable motion robotic system as claimed in claim 11, wherein the hose has a helical ribbing.

18. The programmable motion robotic system as claimed in claim 11, wherein the hose includes at least three joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose defines a plane that includes a respective direction that is generally parallel with an axis of rotation of the respective joint.

19. The programmable motion robotic system as claimed in claim 11, wherein the hose includes no portions of the hose that is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose defines a plane that includes a respective direction that is generally not parallel with an axis of rotation of the respective joint.

20. The programmable motion robotic system as claimed in claim 11, wherein the end effector includes a flexible bellows.

21. A programmable motion robotic system comprising a plurality of arm sections that are joined one to another at a plurality of joints to form an articulated arm; and a hose coupling an end effector of the programmable motion robotic system to a vacuum source, said hose being attached, in a joint portion of the hose, to at least two arm sections of the plurality of arm sections with a joint of the plurality of joints therebetween such that the joint portion of the hose defines a plane that includes a direction that is generally parallel with an axis of rotation of the joint.

22. The programmable motion robotic system as claimed in claim 21, wherein the hose includes at least two joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose each defines a plane that includes a respective direction that is generally parallel with an axis of rotation of the respective joint.

23. The programmable motion robotic system as claimed in claim 21, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a flow rate of at least 100 cubic feet per minute.

24. The programmable motion robotic system as claimed in claim 21, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a vacuum pressure of no more than 50,000 Pascals below atmospheric.

25. The programmable motion robotic system as claimed in claim 21, wherein the hose has an inner diameter of at least 1 inch.

26. The programmable motion robotic system as claimed in claim 21, wherein the hose has an inner diameter of at least 3 inches.

27. The programmable motion robotic system as claimed in claim 21, wherein the hose has a helical ribbing.

28. The programmable motion robotic system as claimed in claim 21, wherein the hose includes at least three joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose defines a plane that includes a respective direction that is generally parallel with an axis of rotation of the respective joint.

29. The programmable motion robotic system as claimed in claim 21, wherein the hose includes no portions of the hose that is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose defines a plane that includes a respective direction that is generally not parallel with an axis of rotation of the respective joint.

30. The programmable motion robotic system as claimed in claim 21, wherein the end effector includes a flexible bellows.

31. A method of providing a high flow vacuum source to an end effector of a programmable motion robotic system, said method comprising: providing a hose that couples the end effector to a vacuum source, the hose including a joint portion of the hose proximate a joint of the programmable motion robotic system; and rotating at least one arm section attached to the joint about an axis, wherein the joint portion of the hose defines a plane that includes a direction that is generally parallel with the axis of rotation of the joint.

32. The method as claimed in claim 31, wherein the hose includes at least two joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose each defines a plane that includes a respective direction that is generally parallel with an axis of rotation of the respective joint.

33. The method as claimed in claim 31, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a flow rate of at least 100 cubic feet per minute.

34. The method as claimed in claim 31, wherein the vacuum source provides, via the hose, a vacuum at the end effector having a vacuum pressure of no more than 50,000 Pascals below atmospheric.

35. The method as claimed in claim 31, wherein the hose has an inner diameter of at least 1 inch.

36. The method as claimed in claim 31, wherein the hose has an inner diameter of at least 23 inches.

37. The method as claimed in claim 31, wherein the hose has a helical ribbing.

38. The method as claimed in claim 31, wherein the hose includes at least three joint portions of the hose, each of which joint portion of the hose is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose defines a plane that includes a respective direction that is generally parallel with an axis of rotation of the respective joint.

39. The method as claimed in claim 31, wherein the hose includes no portions of the hose that is attached to at least two adjacent arm sections mutually attached to a respective joint such that the joint portions of the hose defines a plane that includes a respective direction that is generally not parallel with an axis of rotation of the respective joint.

40. The method as claimed in claim 31, wherein the end effector includes a flexible bellows.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The following may be further understood with reference to the accompanying drawings in which:

[0015] FIG. 1 shows an illustrative diagrammatic view of two large diameter vacuum hoses;

[0016] FIGS. 2A-2D show illustrative diagrammatic views of two arm sections of an articulated arm with a section of a hose attached to the arm sections of the prior art with the hose section inside of a bend joint;

[0017] FIGS. 3A and 3B show illustrative diagrammatic views of two arm sections of an articulated arm with a section of a hose attached to the arm sections of the prior art with the hose section outside of a bend joint;

[0018] FIGS. 4A and 4B show illustrative diagrammatic views of two arm sections of an articulated arm with a section of a hose attached the arm sections in accordance with an aspect of the invention showing two different views of the arm sections in the same position;

[0019] FIGS. 5A and 5B show illustrative diagrammatic views of two arm sections of an articulated arm with a section of a hose attached the arm sections in accordance with an aspect of the invention showing the hose section bent toward the viewing direction;

[0020] FIGS. 6A and 6B show illustrative diagrammatic views of two arm sections of an articulated arm with a section of a hose attached the arm sections in accordance with an aspect of the invention showing the hose section bent away from the viewing direction;

[0021] FIG. 7 shows an illustrative graphical representation of joint angle verses potential energy due to bending for in-plane and out-of-plane hose bending;

[0022] FIG. 8 shows an illustrative diagrammatic view of an articulated arm system showing an axis of rotation of a joint B and a plane C in which a hose section is positioned;

[0023] FIG. 9 shows an illustrative diagrammatic view of the articulated arm system of FIG. 8 showing the axis of rotation of the same joint shown in FIG. 8 showing planes running perpendicular to the joint;

[0024] FIG. 10 shows an illustrative diagrammatic rear view of the articulated arm system of FIG. 8;

[0025] FIG. 11 shows an illustrative diagrammatic rear view of the articulated arm system of FIG. 10 with a plurality of arm sections having been rotated about a plurality of joints;

[0026] FIG. 12 shows an illustrative diagrammatic right side view of the articulated arm system of FIG. 10;

[0027] FIG. 13 shows an illustrative diagrammatic right side view of the articulated arm system of FIG. 11;

[0028] FIG. 14 shows an illustrative diagrammatic top view of the articulated arm system of FIG. 10;

[0029] FIG. 15 shows an illustrative diagrammatic top view of the articulated arm system of FIG. 11;

[0030] FIG. 16 shows an illustrative diagrammatic front view of the articulated arm system of FIG. 10;

[0031] FIG. 17 shows an illustrative diagrammatic front view of the articulated arm system of FIG. 11;

[0032] FIG. 18 shows an illustrative diagrammatic left side view of the articulated arm system of FIG. 10;

[0033] FIG. 19 shows an illustrative diagrammatic left side view of the articulated arm system of FIG. 11;

[0034] FIG. 20 shows an illustrative diagrammatic rear view of the articulated arm system of FIG. 8 showing a hose section plane E that is parallel with an axis of rotation D of an associated joint;

[0035] FIG. 21 shows an illustrative diagrammatic view of two arm sections showing a hose section plane F that is parallel with an axis of rotation G of an associated joint;

[0036] FIG. 22 shows an illustrative diagrammatic enlarged side view of the articulated arm system of FIG. 20;

[0037] FIGS. 23A-23D show illustrative diagrammatic views of an articulated arm system in a working environment moving objects while employing a hose routing system in accordance with an aspect of the present invention;

[0038] FIG. 24 shows an illustrative diagrammatic rear view of the articulated arm system of FIG. 8 employing fixed position hose mounts in accordance with an aspect of the invention;

[0039] FIG. 25 shows an illustrative diagrammatic rear view of the articulated arm system of FIG. 8 employing swivel hose mounts in accordance with an aspect of the invention;

[0040] FIG. 26 shows an illustrative diagrammatic view of an articulated arm system in accordance a further aspect of the invention employing a routing scheme that includes a hose section that spans a plurality of arm sections and joints, showing a hose section plane I that is parallel with an axis of rotation H of a joint of the plurality of joints; and

[0041] FIG. 27 shows an illustrative diagrammatic view of an articulated arm system of FIG. 26 employing the routing scheme that includes the hose section that spans the plurality of arm sections and joints, showing planes running perpendicular to the joint of the plurality of joints.

[0042] The drawings are shown for illustrative purposes only.

DETAILED DESCRIPTION

[0043] In accordance with various embodiments, the invention provides a method of mounting a large diameter cabling or hose on a multi-link mechanical system that (1) minimizes changes to the bending of a hose during motion, and (2) minimizes the maximum bending of such a hose in potential robot configurations.

[0044] Instead of bending in the plane of the motion of the rotating links (articulated arm sections), the hose is mounted in a way that it bends out of the plane of the articulated arm sections' motion. As shown in FIGS. 4A and 4B from two views, a hose section 46 is attached to two arm sections 40, 42 at two ends by any of (1) rigidly with a fixed mount; (2) on a swivel mount allowed to rotate about an axis; or (3) on an actively actuated mount. The arm sections 40, 42 are each coupled to a joint 44. If mounted rigidly, i.e., case (1), the tangents to the hose at these points is nearly perpendicular to the plane of motion, or set at an angle that reduces both the maximum bending, and maximum change in bending. In the latter two cases (2) or (3), the axes of the rotation for passive or active swiveling are nearly parallel to the plane of the motion.

[0045] As the attachment points are positioned closed to each other, the hose tangents at the attachment points become nearer to perpendicular to the plane of motion. As the attachment points are positioned more distant from each other, the hose tangent points become nearer to the plane of the link motion. In accordance with further aspects of the invention, as the sections rotate about a joint's axis of rotation, the hose slides through and/or rotates about attached mounts that swivel about mount axes of rotation.

[0046] FIGS. 5A and 5B show arm sections 50, 52 of an articulated arm programmable motion robotic system that are coupled to a joint 54, with a joint portion of a hose 56 attached to the arm sections. The joint potion of the hose 56 remains out of plane with respect to the joint 54. FIGS. 6A and 6B show similar arm sections 60, 62 that are coupled to a joint 64 with a joint hose portion 66 on a far side (with respect to FIGS. 5A and 5B) of the joint 64. As shown in FIGS. 5A-6B, the joint hose section is not required to be on any particular side of the joint.

[0047] Though there remains a change in the bending during a motion, the degree of change in bending is lower than in a common hose routing scheme, as shown before. The strainor change in bendingover the course of the motions is lower than with the in-plane scheme.

[0048] FIG. 7 shows a graphical representation of the total bending energy of the two schemes vs. the angle of rotation between arm sections. The in-plane scheme has higher hose stress and change in hose stress over the different motions. In particular, FIG. 7 shows at 70 the amount of potential energy (in Joules) due to bending over joint angles in a conventional in-plane routing technique in which a hose is mounted to arm sections such that it rotates in the plane of the joint. FIG. 7 shows at 72 the amount of potential energy (in Joules) due to bending over joint angles in a system incorporating routing in accordance with aspects of the present invention. Note that the range of potential energy values for the out-of-plane routing, r.sub.1, is substantially less than the range of potential energy values for the in-plane routing, r.sub.2. Although the hose will still experience some stress, the range of change in such stress (as well as the highest amount of such stress) will be significantly less.

[0049] FIG. 8 shows at 80 an articulated arm programmable motion robotic system that includes a vacuum end effector 82 (e.g., including a flexible bellows) that is coupled to a vacuum source 84 by a hose 86. The system includes a base 88 that supports an articulated arm 90 having arm sections 92, 94, 96 and 98. A section of the hose, hose section 100, is coupled to adjacent arm sections 92, 94 that are each coupled to a joint 102 by which the arm sections 92, 94 may be rotated about an axis B. The joint portion of the hose 100 is mounted to define a plane 104 (e.g., through the center of the hose section 100), and such plane 104 is defined by having a plurality of directions as shown at 106. In accordance with an aspect of the invention, one of these directions (C as labelled) is parallel with the axis B.

[0050] FIG. 9 shows the system 80 that includes the articulated arm programmable motion robotic system that includes the vacuum end effector 82 that is coupled to the vacuum source 84 by the hose 86. Again, the system includes the base 88 that supports the articulated arm 90 having arm sections 92, 94, 96 and 98. Similarly, the section of the hose 100 is coupled to adjacent arm sections 92, 94 that are each coupled to the joint 102 by which the arm sections 92, 94 may be rotated about an axis B as discussed with respect to FIG. 8. During such rotation of the arm sections 92, 94 at the joint 102, the arm sections 92, 94 will define a plurality of planes as shown at 110. The plurality of planes 110 span the width of the joint 102. The joint portion of the hose 100 is mounted such that the joint portion of the hose 100 lies substantially outside of the plurality of planes 110.

[0051] In accordance with various aspects of the invention, the vacuum at the end effector may have a flow rate of at least 100 cubic feet per minute, and a vacuum pressure of no more than 50,000 Pascals below atmospheric. The hose may have an inner diameter of at least 1 inch (or at least 3 inches), and may include a helical ribbing as discussed above.

[0052] To better show the system from multiple angles, FIG. 10 shows a back perspective view of the system 80, FIG. 12 shows a left side view of the system 80, FIG. 14 shows a top view of the system 80, FIG. 16 shows a front view of the system 80 and FIG. 18 shows a left side perspective view of the system 80. FIGS. 11, 13, 15, 17 and 19 shows a system 80 in which the articulated arm of the system of FIGS. 10, 12, 14, 16 and 18 is moved such that the arm sections are extended in a single direction (to further show the hose routing). The components of the system of FIGS. 11, 13, 15, 17 and 19 are the same as those of FIGS. 10, 12, 14, 16 and 18. In particular, FIG. 11 shows a back perspective view of the system 80, FIG. 13 shows a right side view of the system 80, FIG. 15 shows a top view of the system 80, FIG. 17 shows a front view of the system 80 and FIG. 19 shows a left side perspective view of the system 80.

[0053] The hose routing of embodiments of the invention may be applied to a plurality of arm sections of an articulated arm system. FIG. 20, for example, shows a system 80 that includes a base 88 that supports an articulated arm 90 having arm sections 92, 94, 96 and 98. A section of the hose, hose section 100, is coupled to adjacent arm sections 94, 96 that are each coupled to a joint 112 by which the arm sections 94, 96 may be rotated about an axis D. The joint portion of the hose 100 is mounted to define a plane 114 (e.g., through the center of the hose section 100), and such plane 114 is defined by having a plurality of directions as shown at 116. In accordance with an aspect, one of these directions (E as labelled) is parallel with the axis D. In such a system, both the hose section 100 and the hose section 100 of the hose 86 may be routed in accordance with various aspects of the present invention. FIG. 22 shows a close-up view of a portion of the system 80 of FIG. 20. As may be seen in FIG. 22, the hose section 100 defines a plane 114, for example, through a longitudinal center of the curved hose section 110.

[0054] FIG. 21 shows an example of such out-of-plane routing with a joint and arm sections as shown in FIGS. 4A-6B. Such a system includes arm sections 120, 122 of an articulated arm programmable motion robotic system that are coupled to a joint 124, with a joint portion of a hose 126 attached to the arm sections. The joint potion of the hose 126 remains out of plane with respect to the joint 124. Again the plane F shown at 128 includes a direction that is parallel with an axis of rotation G of the joint 124.

[0055] FIGS. 23A-23D show the articulated arm programmable motion robotic system 80 that includes the vacuum end effector 82 that is coupled to the vacuum source 84 by the hose 86. The system includes the base 88 that supports the articulated arm 90 having arm sections 92, 94, 96 and 98. The section of the hose 100 is coupled to adjacent arm sections 92, 94 that are each coupled to the joint 102 by which the arm sections 92, 94 may be rotated. The joint portion of the hose 100 is mounted to define a plane that includes a direction that is parallel with the axis of rotation of the joint as discussed above. Further, the joint portion of the hose 100 lies substantially outside of the plurality of planes 110 defined by movement of the arm sections 92, 94 as also discussed above. Similarly, section of the hose 100 is coupled to adjacent arm sections 94, 96 that are each coupled to a joint by which the arm sections 94, 96 may be rotated about an axis meeting the above requirements.

[0056] With reference to FIGS. 23A-23D, the articulated arm system may be employed, under control of one or more computer processing system(s) 130 to move from one object 132 (FIG. 23A) to another 134 (FIGS. 23B and 23C), and to then lift the new object 134. Note that when the arm sections 94 and 96 are moved to be very close to each other (shown in FIG. 23C), the hose section 100 remains relatively free of bending and therefore stress.

[0057] The hose attachments may be fixed, may provide swiveling, and/or may provide for translation of the hose through the attachments in various aspects of the invention. The swivel attachments may also have more than one degree of freedom (DOF). While, the swivel may only allow rotation of the hose about an axis that is in the plane of the motion, a swivel joint may accommodate other additional DOFs including: the hose may twist through the mount to reduce torsion on the hose, the hose may slip through the mount to lengthen or shorten the hose segment between attachment points, and the attachment may permit small deflections of the rotation axis also to reduce total bending energy.

[0058] FIGS. 24 and 25 show articulated arm programmable motion robotic systems 140 and 140 that include the vacuum end effector 82 that is coupled to the vacuum source 84 by the hose 86. The systems include the base 88 that supports the articulated arm 90 having arm sections 92, 94, 96 and 98. The section of the hose 100 is coupled to adjacent arm sections 92, 94 that are each coupled to the joint 102 by which the arm sections 92, 94 may be rotated. Again, the joint portion of the hose 100 is mounted to define a plane that includes a direction that is parallel with the axis of rotation of the joint as discussed above. Further, the joint portion of the hose 100 lies substantially outside of the plurality of planes defined by movement of the arm sections 92, 94 as also discussed above. Similarly, section of the hose 100 is coupled to adjacent arm sections 94, 96 that are each coupled to a joint by which the arm sections 94, 96 may be rotated about an axis meeting the above requirements.

[0059] The hose attachments 142 of the system 140 are fixed position, yet may optionally permit translation of the hose through the attachments as shown by the double ended arrows. The hose attachments 144 of the system 140 are swivel attachments that may rotate with the hose, and further may permit translation of the hose through the attachments as also shown by the double ended arrows. Note that the hose 86 in FIG. 25 with the swivel attachments, appears to be more free of stress than the hose in FIG. 24, and permits the hose to assume a wider variety of positions. In accordance with various aspects, the hose may be coupled to each attachment with a coupling that permits each hose section to rotate about the hose's central axis.

[0060] The system may also provide hose routing in accordance with aspects of the invention including hose attachments on non-adjacent arm sections. FIG. 26, for example, shows at 180 an articulated arm programmable motion robotic system that includes a vacuum end effector 182 that is coupled to a vacuum source 184 by a hose 186. The system includes a base 188 that supports an articulated arm 190 having arm sections 192, 194, 196 and 198. A section of the hose, hose section 200, is coupled to non-adjacent arm sections 192, 196 that share a joint 202 therebetween. The joint 202 may be rotated about an axis H. The joint portion of the hose 200 is mounted to define a plane 204 (e.g., through the center of the hose section 200), and such plane 204 is defined by having a plurality of directions as shown at 206. In accordance with an aspect, one of these directions (I as labelled) is parallel with the axis H.

[0061] FIG. 27 shows the system 180 that includes the articulated arm programmable motion robotic system that includes the vacuum end effector 182 that is coupled to the vacuum source 184 by the hose 186. Again, the system includes the base 188 that supports the articulated arm 190 having arm sections 192, 194, 196 and 198. Similarly, the section of the hose 200 is coupled to non-adjacent arm sections 192, 196 that share the joint 202 therebetween. The joint 202 may be rotated about the axis H as discussed with respect to FIG. 26. During such rotation of the arm sections 194, 196 about the joint 202, the arm sections 192, 194 will define a plurality of planes as shown at 210. The plurality of planes 210 span the width of the joint 202. The joint portion of the hose 200 is mounted such that the joint portion of the hose 200 lies substantially outside of the plurality of planes 210.

[0062] Hose routing approaches of various embodiments of the invention allow for a chain of such kinds of attachments and hose segments to be provided that would exploit out-of-plane motions for a multi-link articulated arm programmable motion robotic system, with the objective of minimizing the maximum bending energy, and reducing the amount of cyclic loading to which the hose would be subjected.

[0063] Those skilled in the art will appreciate that modifications and variations may be made the above disclosed embodiments without departing from the spirit and scope of the present invention.