Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

New Family of RPR-Equivalent Parallel Mechanisms:Design and Application

Parallel mechanisms（PMs） have been used as skeletons or end-effectors in various advanced manufacturing equipment. Compared with their serial counterparts, PMs offer high rigidity, good dynamic response, and large payload capability.

Gravity-Based Kinetostatic Modeling of Parallel Manipulators Using Screw Theory

The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.