CLASSIFICATION OF DESIGNS FOR RRSS LINKAGES

This paper presents a classification of designs for an RRSS spatial linkage. The analysis of this linkage results in a wellknown constraint equation that defines the configuration of the chain for given values of the input crank angle. The range of movement of this crank is defined by a condition on the values of the input crank angle. This condition is a quartic polynomial and its real roots provide a way to classify the movement of the RRSS linkage. This condition yields as many as four real roots, which means the input crank angle of an RRSS linkage can have up to four limits to its range of movement. We use three polynomial discriminants obtained from this quartic condition in order to find explicit conditions for all cases available for the movement of the input crank. Examples for each case are provided. This result provides a means to classify the RRSS linkage, and is important for the computer-aided-design of these spatial mechanisms.