On instantaneous translation in the couplers of spatial linkages

An important consideration for designers of machinery is the phenomenon of limiting positions for an output link of a planar mechanism, whereby the member’s range of motion can be defined. Less obviously discernible in this context are configurations for which an intermediate link instantaneously ceases to rotate. Such positions assume greater significance in spatial applications where instantaneous translation of a member may more easily permit external procedures to be executed by or upon it. Screw system algebra has been found to be particularly efficacious in the investigation of various aspects of special linkage configurations and it is used here to no less advantage. The scope of the method is clarified by the employment of a series of examples of increasing connectivity-sum.