Exact 3D Path Generation via 3D Cam-Linkage Mechanisms

Abstract

Exact 3D path generation is a fundamental problem of designing a mechanism to make a point exactly move along a prescribed 3D path , driven by a single actuator. Existing mechanisms are insufficient to address this problem. Planar linkages and their combinations with gears and/or plate cams can only generate 2D paths while 1-DOF spatial linkages can only generate 3D paths with rather simple shapes. In this paper, we present a new 3D cam-linkage mechanism, consisting of two 3D cams and five links, for exactly generating a continuous 3D path. To design a 3D cam-linkage mechanism, we first model a 3-DOF 5-bar spatial linkage to exactly generate a prescribed 3D path and then reduce the spatial linkage's DOFs from 3 to 1 by composing the linkage with two 3D cam-follower mechanisms. Our computational approach optimizes the 3D cam-linkage mechanism's topology and geometry to minimize the mechanism's total weight while ensuring smooth, collision-free, and singularity-free motion. We show that our 3D cam-linkage mechanism is able to exactly generate a continuous 3D path with arbitrary shape and a finite number of C 0 points, evaluate the mechanism's kinematic performance with 3D printed prototypes, and demonstrate that the mechanism can be generalized for exact 3D motion generation.