Algebraic synthesis and input-output analysis of 1-DOF multi-loop linkages with a constant transmission ratio between two adjacent parallel, intersecting or skew axes.

• An algebraic synthesis method is proposed to form novel multi-loop linkages for rotation scaling. • Multi-loop planar, spherical, and spatial linkages can be constructed using the proposed method. • The generated linkages can exactly transmit angular motion with prescribed transmission ratios. • Exact angular motion transmission between parallel, intersecting, or skew axes is achieved. • Transmission characteristics of the multi-loop linkages are proved by kinematics analysis. This paper deals with the algebraic synthesis and input-output analysis of one degree-of-freedom (1-DOF) multi-loop planar, spherical, and spatial linkages for increasing or decreasing angular motion with a desired constant transmission ratio between two adjacent parallel, intersecting, and skew axes respectively. Based on the rotation scaling model and motion polynomials over dual quaternions, an algebraic synthesis method including three procedures is proposed to exactly construct novel multi-loop linkages owning arbitrarily prescribed constant transmission ratios and input/output axes. To illustrate this method, several 1-DOF multi-loop planar, spherical, and spatial linkages for rotation scaling are synthesized by designating various input and output axes as well as transmission ratios. Taking some multi-loop planar, spherical, and spatial linkages as examples, input-output analysis is carried out to verify their transmission characteristics. The results demonstrate that the generated 1-DOF multi-loop linkages can indeed transmit motion with prescribed constant transmission ratios and input/output axes. This work provides a framework for further investigation on mechanisms performing specified tasks for motion transmission. [ABSTRACT FROM AUTHOR]