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Efficient kinematics of a 2-1 and 3-1 CDPR with non-elastic sagging cables

Jean-Pierre Merlet 1 
1 HEPHAISTOS - HExapode, PHysiologie, AssISTance et Objets de Service
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Solving the kinematics of CDPR is complex as soon as cable sagging is taken into account. We are considering here CDPRs having 2 cables whose extremities are attached at the same point on the platform (i.e. CDPRs allowing only translational motion). Regarding the cables we assume that they are nonelastic but have a mass so that they will exhibit sagging. We first show that the inverse and direct kinematics (IK and DK) amount to solve a square system of equations. We then show that these systems of equations may be reduced to solving an equation in a single variable that cannot be solved analytically but can easily be solved numerically. Using this result we show that the sagging will play a role on the result of the IK/FK only if the load mass is lower than a threshold. We then present some preliminary results regarding the case of 3 cables which is much more complex: the IK may be reduced to solving an equation in a single variable but this solving is numerically difficult. Here again it seems that sagging may be neglected if the load mass is high enough. We also present a preliminary analysis of the 3-1 case.
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https://hal.inria.fr/hal-03284195
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Submitted on : Monday, July 12, 2021 - 2:05:37 PM
Last modification on : Saturday, June 25, 2022 - 11:51:03 PM
Long-term archiving on: : Wednesday, October 13, 2021 - 7:04:06 PM

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Jean-Pierre Merlet. Efficient kinematics of a 2-1 and 3-1 CDPR with non-elastic sagging cables. CableCon 2021 - 5th International Conference on Cable-Driven Parallel Robots, Jul 2021, Virtual, France. ⟨10.1007/978-3-030-75789-2_1⟩. ⟨hal-03284195⟩

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