Abstract
This work discusses the kinematic characteristics of planar four-bar mechanisms by application of kinematic coefficients. Applying the concept of instant centers and using vector loop equations, we provide alternative proof of Freudenstein's three theorems, the firs two of which may be used to examine the extreme velocity ratio of a four-bar linkage and the third one to characterize the nature of the acceleration coefficient. We further discuss the relationship between the kinematic coefficients of a four-bar linkage and its toggle configuration and then use the relationship to explore the momentary-dwell characteristics of six-bar toggle linkages. Through the concept of kinematic coefficient, we also design polynomial motion curves of a cam mechanism with better kinematic characteristics; the design procedure starts from imposing the constrains of the jerk curve to have some successive zero derivatives at the connection point of each motion interval. Finally, applying Freudenstein's third theorem, we propose a simple graphical method to construct the equivalent four-bar linkage of a disk-cam mechanism; by means of the joint locations of the equivalent linkage, the instantaneous radius of curvature of a disk-cam profile can be readily determined. Two examples are given to illustrate the graphical method.