Abstract
A novel method for force analysis of the overconstrained lower mobility parallel mechanisms (LMPM) is proposed. Firstly, definitions of the constraint wrenches and overconstraint wrenches are put forward. Then, overconstrained LMPMs are classified into two classes based on characteristic of the elastic deformations generated at the end of the supporting limbs, which are limb stiffness decoupled overconstrained LMPM and limb stiffness coupled overconstrained LMPM, respectively. Corresponding to the limb stiffness decoupled and coupled overconstrained LMPMs, stiffness matrix of the supporting limb's overconstraint wrenches and constraint wrenches are introduced and defined respectively. Next, taking the link's spatial composite elastic deformations into account, the stiffness matrix of the supporting limb's overconstraint wrenches or constraint wrenches is established, and general analytical expression for the solution of each supporting limb's overconstraint wrenches or constraint wrenches is derived. Furthermore, the internal relation between the constraint wrenches and the actual joint reactions is discussed. Finally, based on Adams simulation software, a method to set up the force simulation model of the overconstrained LMPM is put forward, and the simulation results and the theoretical calculation ones are basically consistent, which effectively verifies the correctness of the proposed method for force analysis of the overconstrained LMPM.
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