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.
|Journal||Mechanism and Machine Theory|
|Publication status||Published - Oct 2022|
- Closed-loop subchain
- Jacobian analysis
- Nonredundant parallel mechanisms
- Repelling screw system