A Unified Approach to Forward Kinematics for Cable-Driven Parallel Robots Based on Energy

Pott, Andreas; Tempel, Philipp

doi:10.1007/978-3-319-93188-3_46

Cited by 8 publications

(7 citation statements)

References 10 publications

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“…Regarding point 2 the DK problem of CDPRs with ideal cable (no mass, no elasticity) has been addressed in several works [14][15][16][17] but there are much less works on the DK with sagging cables [18][19][20][21][22]. The proposed algorithms either cannot guarantee to find all solutions or are relatively expensive in term of computation time.…”

Section: Introductionmentioning

confidence: 99%

Efficient Kinematics of a 2-1 and 3-1 CDPR with Non-elastic Sagging Cables

Merlet

2021

Mechanisms and Machine Science

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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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Section: Introductionmentioning

confidence: 99%

Efficient Kinematics of a 2-1 and 3-1 CDPR with Non-elastic Sagging Cables

Merlet

2021

Mechanisms and Machine Science

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“…However singularity are crossed during the continuation and are difficult to manage [16,24]. It was recently proposed to solve the DK by looking at the minima of the potential energy of CDPR [25] but finding numerically all these minima is tedious and uncertain.…”

Section: Introductionmentioning

confidence: 99%

Some properties of the Irvine cable model and their use for the kinematic analysis of cable-driven parallel robots

Merlet

2019

Mechanism and Machine Theory

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Cable model has a strong influence on the complexity of the kinematic analysis of cable-driven parallel robots (CDPR). The most complete elasto-static model relies on Irvine equation that takes into account both the elasticity and the deformation of the cable due to its own mass and has been shown to be very realistic. This model is complex, non algebraic and numerically ill-conditioned, thereby leading to difficulties when using it in a kinematic analysis involving several cables. We exhibit some properties of this model that may drastically improve the analysis computation time when used in kinematic studies.

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“…The energy method allows this magnitude to be used to consider either the tension or the linear elongation of the cable or even other physical effects such as electromagnetics. Some methods based on energy have recently been used to solve the forward kinematics, as seen in [35,36].…”

Section: Introductionmentioning

confidence: 99%

Potential Energy Distribution of Redundant Cable-Driven Robot Applied to Compliant Grippers: Method and Computational Analysis

Rodriguez-Barroso

Saltarén

Portilla

et al. 2019

Sensors

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Cable-driven parallel robots with a redundant configuration have infinite solutions for their cable tension distribution to provide a specific wrench to the end-effector. Redundancy is commonly used to increase the workspace and stiffness or to achieve secondary objectives like energetic minimization or additional movements. This article presents a method based on energy distribution to handle the redundancy of cable-driven parallel robots. This method allows the deformation and tension of each link to be related to the total energy available in the parallel robot. The study of energy distribution expression allows deformation, tension, and position to be combined. It also defines the range of tension and deformation that cables can achieve without altering the wrench exerted on the end-effector. This range is used with a passive reconfigurable end-effector to control the position of two grippers attached to some cables which act as compliant actuators. The relationship between the actuators’ energy and their corresponding gripper positions is also provided. In this way, energy measurement from the actuators allows the grasping state to be sensed. The results are validated using multibody dynamic software.

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A Unified Approach to Forward Kinematics for Cable-Driven Parallel Robots Based on Energy

Cited by 8 publications

References 10 publications

Efficient Kinematics of a 2-1 and 3-1 CDPR with Non-elastic Sagging Cables

Efficient Kinematics of a 2-1 and 3-1 CDPR with Non-elastic Sagging Cables

Some properties of the Irvine cable model and their use for the kinematic analysis of cable-driven parallel robots

Potential Energy Distribution of Redundant Cable-Driven Robot Applied to Compliant Grippers: Method and Computational Analysis

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