Optimal counterweight balancing of spatial mechanisms using voxel-based discretizations

摘要

A mechanism exerts forces and moments on its supporting frame, which result in vibration. The aim of counterweight balancing is to reduce this vibration by adding counterweights on the moving mechanism links. This paper shows that, even for the complicated case of spatial mechanisms, finding the counterweight parameters that result in minimal forces and moments under constrained driving torque is an optimization problem that can be reformulated as a convex problem. This reformulation uses voxel-based discretizations, inspired by the typical discretizations used in the area of topology optimization, and results in counterweight shapes that can easily be implemented in practice. The advantages of the proposed methodology in terms of computation time, balancing result and practicality of the counterweights are demonstrated using a literature benchmark consisting of a RSSR - spatial fourbar mechanism.