On the Synthesis of Straight Line, Constant Velocity Scanning Mechanisms

Abstract

This paper presents a kinematic synthesis of constant-velocity, straight-line coupler-point motion of two planar mechanisms. After the derivation of synthesis equations, the numerical results of a grid search to determine the linkage dimensions for maximum constant velocity, with minimal straight line error, are presented. Plots of acceleration magnitude, transmission angles, and transverse velocity are presented as a function of the percentage of the constant velocity portion of a cycle of input motion. For a 5R2P Stephenson 6-bar linkage, normalized velocity errors as small as 2 percent can be maintained over 40 percent, or more, of the input cycle. A 7R Watt 6-bar linkage, while not achieving quite as high values as the 5R2P linkage, nevertheless can maintain normalized velocity errors as low as 2.5 percent over as much as 39 percent of the input cycle. These levels of performance must be weighed against unfavorable transmission angles, and in many cases, other undesirable effects, such as large accelerations and large transverse travel. The results show that, in order to maintain minimally acceptable transmission angle requirements, the velocity error and scan fraction requirements may be as little as 2.0 percent and as much as 35 percent, respectively.