IEEE Robotics & Automation Magazine - September 2022 - 119

diamond shaft can be used as the rotation axis to establish the
moment balance equation:
)
F FFF FF FFF F
T TTT TT TTT F
12 312 ^
12 312 ^
where ,F1
F ,2 and F3
+++ +=- +++ +
+++ +=- +++ +
ty of the rigid body, FC1
and FP2
and FS2
are the cable tensions, FG
and FC2
SS GP PCC
SS GP PC C
1 212h
12 12h
,
(19)
is the gravirepresent
the lateral pressure
that is generated by a cable that passes through the
rigid body, FP1
mond shaft of the postsequence rigid body to support it,
FS1
are the pressures from the diaare
the support from the presequence rigid
body, and T is the torque that is generated by the corresponding
force.
By starting from the rigid body at the end of the manipulator,
solving the equation in turn, and putting the result into
the rigid body's balance equation, this technique can solve
the tension for all of the cables. Therefore, for question 1,
during each step of path planning, by using the current pose
and (19), the relative magnitude of the current cable tension
can be obtained, and the largest one can be determined.
For question 2, in the previous work, we discovered and
verified a characteristic of the cable tension according to the
tension model. If a rigid body rotates slightly while the size
and direction of the load are almost unchanged, the change in
-100
-200
-1,000
-800
-800
-600
-600
-400
-400
-200
(a)
200
400
-50
-100
-150
-200
-250
-800
-600
-400
-200
200
(c)
400
100
200
(d)
600
200
100
200
-50
-100
-150
-200
-250
-600
-400
-200
200
400
100
(b)
400
200
-200
200
100
-100
-200
-1,000
Figure 17. A comparison of the moving process. In each part of the figure, the postures of the dashed manipulator are obtained by normal
planning, while the solid are obtained by tension-optimization planning. Posture at (a) the beginning of the path, (b) one-third of the path,
(c) two-thirds of the path, and (d) the end of the path.
SEPTEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
119

IEEE Robotics & Automation Magazine - September 2022

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2022

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