Optimum design of a spherical quasi-homokinetic linkage for motion transmission between orthogonal axes

Abstract

Homokinetic motion transmission between two shafts with axes intersecting at right angles is a recurrent problem; the term quasi-homokinetic indicates that a constant 1:1 velocity ratio between the input and output is the design target, even though this cannot be fully met with a four-bar linkage. A four-bar spherical linkage is optimally designed, which performs “homokinetically” with minimum error through a 120° rotation of its input link, large enough for one specific robotics application. This is done via: (i) minimizing the root-mean-square value of the design error, i.e., the residual of the synthesis equations at the prescribed set of input values; and (ii) directly minimizing the structural error, i.e., the deviation of the generated output angles from the prescribed set. The novelty of the first method lies in that it provides all stationary points, and hence, the global minimum; finding a continuum of minima leaves ample room for maximizing the transmission quality. Further, the effect of data-set cardinality on the structural error is analyzed, which is then minimized directly. A new mechanism is thus obtained with a minimum structural error, but with a slightly compromised transmission quality.