A Dynamics-Based Method for Determining the Local Finite Mobility of Single-loop Spatial Mechanisms

This paper proposes a method for calculating the local finite mobility of single-loop spatial mechanisms based on modal analysis. Using spanning tree-based multibody dynamics, the single-loop spatial mechanism is modeled as a tree-like kinematic chain with serial chains closed by the constraints represented by a spring force model. The dynamic model is linearized using Taylor expansion. The stiffness matrix is then yield. The correspondence between vibrating/non-vibrating generalized coordinates and the nonzero/zero eigenvalues in the stiffness matrix is clarified. The mobility of the single loop spatial mechanism is then determined by the number of zero eigenvalues in the stiffness matrix. The method is then validated and analyzed by calculating the DOF of Sarrus mechanism, Bennett mechanism, 3-mode 7R mechanism, a mechanism with special parameters and a variable-DOF 8R mechanism. One contribution is that this work enhances spanning-tree-based dynamic modeling by analyzing joint selection strategies and introducing spring forces to replace kinematic constraints. The Other contribution is that based on the linearized model, a modal analysis framework is established to determine the mobility of single-loop spatial mechanisms.