Mobility of overconstrained parallel mechanisms with reconfigurable end-effectors

TY - JOUR

T1 - Mobility of overconstrained parallel mechanisms with reconfigurable end-effectors

AU - Lambert, Patrice

AU - Da Cruz, Lyndon

AU - Bergeles, Christos

N1 - Funding Information: This work was supported by an ERC Starting Grant [ 714562 ], the Wellcome/EPSRC Centre for Medical Engineering [ WT 203148/Z/16/Z ], and the National Institute for Health Research; Invention for Innovation [ II-LB-0716-20002 ]. Publisher Copyright: © 2022 Elsevier Ltd

PY - 2022/5

Y1 - 2022/5

N2 - Reconfigurable parallel mechanisms have legs or end-effectors with additional degrees of freedom or with the ability to change their mobility. This allows them to reconfigure into a variety of conventional parallel mechanisms. One type of reconfigurable parallel mechanism can be obtained by replacing the end-effector with a closed-loop linkage. The parts of this linkage that are connected to the legs may be considered as the end-effectors, having their own mobility relative to the base and a coupled mobility with each other. Classical methods for mobility analysis cannot be directly applied to this type of mechanism. This article presents a general method to calculate and represent the coupled mobility of the multiple end-effectors using nullspace operations on a matrix of mobility. The nullspace approach provides an efficient way to calculate the mobility in a closed-loop chain while the matrix of mobility allows for calculating the multiple end-effectors mobility interaction. The general method can be performed analytically to obtain insights on the mechanism in any configuration, or algorithmically to obtain numerical values of the mobility in a particular configuration. Two illustrative examples showcasing the method are presented.

AB - Reconfigurable parallel mechanisms have legs or end-effectors with additional degrees of freedom or with the ability to change their mobility. This allows them to reconfigure into a variety of conventional parallel mechanisms. One type of reconfigurable parallel mechanism can be obtained by replacing the end-effector with a closed-loop linkage. The parts of this linkage that are connected to the legs may be considered as the end-effectors, having their own mobility relative to the base and a coupled mobility with each other. Classical methods for mobility analysis cannot be directly applied to this type of mechanism. This article presents a general method to calculate and represent the coupled mobility of the multiple end-effectors using nullspace operations on a matrix of mobility. The nullspace approach provides an efficient way to calculate the mobility in a closed-loop chain while the matrix of mobility allows for calculating the multiple end-effectors mobility interaction. The general method can be performed analytically to obtain insights on the mechanism in any configuration, or algorithmically to obtain numerical values of the mobility in a particular configuration. Two illustrative examples showcasing the method are presented.

UR - http://www.scopus.com/inward/record.url?scp=85123942224&partnerID=8YFLogxK

U2 - 10.1016/j.mechmachtheory.2022.104722

DO - 10.1016/j.mechmachtheory.2022.104722

M3 - Article

SN - 0094-114X

VL - 171

SP - 1

EP - 20

JO - Mechanism and Machine Theory

JF - Mechanism and Machine Theory

IS - 104722

M1 - 104722

ER -