Mobility of overconstrained parallel mechanisms with reconfigurable end-effectors

Patrice Lambert*, Lyndon Da Cruz, Christos Bergeles

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
53 Downloads (Pure)


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.

Original languageEnglish
Article number104722
Pages (from-to)1-20
JournalMechanism and Machine Theory
Issue number104722
Publication statusPublished - May 2022


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