TRACING KINEMATIC PATHS AND LIMIT POINTS OF PIN-BAR MECHANISMS BY A GEOMETRICAL APPROACH

The kinematic analysis of pin-bar mechanisms is carried out from purely geometrical views. Based on geometrical conditions, the kinematic governing equation of mechanism displacement is established. An improved numerical strategy is developed to calculate the kinematic paths of pin-bar mechanisms. The mathematical property of the limit point in kinematic path is clarified. When a joint in pin-bar mechanism reaches its kinematic limit point, its corresponding components in all modes of mechanism displacements are proved to be equal to zero. This characteristic can be adopted as a criterion to determine and numerically trace the limit point of kinematic path. Furthermore, a special geometrical phenomenon of limit configuration is probed and explained theoretically. Two numerical examples are employed to investigate the accuracy and validity of the method put forward in this paper.