Algebraic synthesis of single-loop 6R spatial mechanisms for constant velocity transmission between two adjacent parallel, intersecting or skew axes

This paper addresses the algebraic synthesis of novel single-loop 6R spatial mechanisms, enabling constant -1:1 or 1:1 velocity ratio transmission between two adjacent axes, whether parallel, intersecting, or skew. Based on the motion polynomial over dual quaternions, an algebraic synthesis method including four steps is presented to construct and optimize single-loop 6R spatial mechanisms with a constant transmission ratio of -1:1 or 1:1 between arbitrarily designated input and output axes. Using this method, several novel single-loop 6R spatial mechanisms for constant velocity transmission are constructed by designating different poses and rotation directions of the input and output axes. Kinematics analysis of single-loop 6R spatial mechanisms is implemented to verify their transmission characteristics. The results reveal that the generated 1-DOF single-loop 6R novel mechanisms can indeed transmit motion with a constant transmission ratio of -1:1 or 1:1 between two adjacent parallel, intersecting, or skew axes. This work provides a framework for further investigation on single-loop mechanisms with special transmission characteristics.