A General Spatial Multi-Loop Linkage Optimization Model For Motion Generation With Static Loading

A general spatial multi-loop linkage optimization model for the inverse problem of defect-free motion generation is formulated and demonstrated in this work. The particular linkage of focus is the Revolute-Spherical-Spherical-Revolute-Spherical-Spherical joint (or RSSR-SS) linkage: one of the most basic spatial multi-loop linkages in terms of construction and kinematics. With this optimization model, the RSSR-SS linkage dimensions required to approximate precision positions are calculated along with the driving link torque required to achieve static equilibrium for precision position forces. The optimization model also includes constraints to eliminate order, branch and circuit defects-defects that are common in classical dyad-based dimensional synthesis. Therefore, the novelty of this work is the development of a general optimization model for RSSR-SS motion generation with static loading that simultaneously considers order, branch and circuit defect elimination. This work conveys both the benefits and drawbacks realized when implementing the RSSR-SS optimization model on a personal computer using the commercial mathematical analysis software package Matlab.