A repelling-screw-based approach for the construction of generalized Jacobian matrices for nonredundant parallel manipulators

Wang，Kun1; Dong，Huixu2; Spyrakos-Papastavridis，Emmanouil1; Qiu，Chen1,3; Dai，Jian S.1,4

2022-10-01

10.1016/j.mechmachtheory.2022.105009

MECHANISM AND MACHINE THEORY   影响因子和分区

0094-114X

1873-3999

This paper presents a unified and generalized approach for the construction of Jacobian matrices for general, nonredundant parallel manipulators that possess serial and/or mixed-topology limbs. Using linear algebra, a method for the calculation of repelling screws is proposed, based upon which the underlying correlations amongst the screws (twists and wrenches) that correspond to both the permitted, and constrained, motions of general mechanisms are identified and analyzed. The effect of linear combinations on the repelling screw system is revealed, and further used to determine the constraint wrenches/twists of a parallel manipulator and its limbs. By means of utilising repelling screws, the dualities in parallel and serial mechanisms are revisited and extended. Furthermore, a simple and unified method for the identification of unknown twists and wrenches is proposed, based upon which an intuitive and systematic approach for the formulation of generalized Jacobian matrices for nonredundant parallel manipulators is derived. The generalized multilevel hierarchical Jacobian contains complete constraint, singularity, kinematics, and statics information at both limb and platform levels. A number of provided examples demonstrate the effectiveness and application of the proposed approach.

Closed-loop subchain Duality Jacobian analysis Nonredundant parallel mechanisms Repelling screw system

SCI ; EI

英语

其他

Engineering

Engineering, Mechanical

WOS:000862939600003

PERGAMON-ELSEVIER SCIENCE LTD

20223112468569

Jacobian matrices ; Manipulators ; Mechanisms ; Tools

Mechanisms:601.3 ; Small Tools and Hardware:605 ; Algebra:921.1

ENGINEERING

2-s2.0-85135110097

Scopus

1.Centre for Robotics Research,King's College London,London,WC2R 2LS,United Kingdom
2.School of Mechanical Engineering,Zhejiang University,Hangzhou,310027,China
3.Maider Medical Industry Equipment Co.,ltd.,China
4.Shenzhen Key Laboratory of Biomimetic Robotics and Intelligent Systems,SUSTech Institute of Robotics,Southern University of Science and Technology,Shenzhen,518055,China

Wang，Kun,Dong，Huixu,Spyrakos-Papastavridis，Emmanouil,et al. A repelling-screw-based approach for the construction of generalized Jacobian matrices for nonredundant parallel manipulators[J]. MECHANISM AND MACHINE THEORY,2022,176.

Wang，Kun,Dong，Huixu,Spyrakos-Papastavridis，Emmanouil,Qiu，Chen,&Dai，Jian S..(2022).A repelling-screw-based approach for the construction of generalized Jacobian matrices for nonredundant parallel manipulators.MECHANISM AND MACHINE THEORY,176.

Wang，Kun,et al."A repelling-screw-based approach for the construction of generalized Jacobian matrices for nonredundant parallel manipulators".MECHANISM AND MACHINE THEORY 176(2022).