TY - JOUR
T1 - A repelling-screw-based approach for the construction of generalized Jacobian matrices for nonredundant parallel manipulators
AU - Wang, Kun
AU - Dong, Huixu
AU - Spyrakos-Papastavridis, Emmanouil
AU - Qiu, Chen
AU - Dai, Jian S.
N1 - Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2022/10
Y1 - 2022/10
N2 - 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.
AB - 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.
KW - Closed-loop subchain
KW - Duality
KW - Jacobian analysis
KW - Nonredundant parallel mechanisms
KW - Repelling screw system
UR - http://www.scopus.com/inward/record.url?scp=85135110097&partnerID=8YFLogxK
U2 - 10.1016/j.mechmachtheory.2022.105009
DO - 10.1016/j.mechmachtheory.2022.105009
M3 - Article
AN - SCOPUS:85135110097
SN - 0094-114X
VL - 176
JO - Mechanism and Machine Theory
JF - Mechanism and Machine Theory
M1 - 105009
ER -