Design of Quick-Returning R-S-S-R Mechanisms

An algebraic method is presented to synthesize quick-returning R-S-S-R mechanisms which satisfy the given time-ratio and follower oscillation angle requirements. In these designs, the three parameters, which define the follower spheric joint, satisfy a quadratic condition. When the shaft angle between the input and output shafts is zero, this quadratic condition reduces to the equation of a circle which is a familiar classical result for the planar case. The solution space for the quick-returning R-S-S-R linkage is such that, for each set of choices for crank length a 2 , follower axial distance S 4 , and initial follower angle φ0 , there are four sets of follower length a 4 , initial crank angle θ0 , crank axial distance S 2 , and coupler length a 3 . These designs are screened so that they do not have branch defect, have transmission angle values in a given range, and have reasonable link length proportions.