Spatial Straight Line Linkages by Factorization of Motion Polynomials
This work addresses the design of spatial linkages for mechanical engineering, but it appears incremental as it builds on existing factorization methods to produce specific linkage configurations.
The paper tackled the problem of constructing overconstrained spatial linkages with a straight line trajectory by using factorization of motion polynomials, resulting in linkages such as those with four revolute and two prismatic joints and a notable one with seven revolute joints performing a Darboux motion.
We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight line trajectory. Unlike previous examples, the end-effector motion is not translational and the link graph is a cycle. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.