On Calculating the Degrees of Freedom or Mobility of Overconstrained Linkages: Single-Loop Exceptional Linkages

Abstract

This paper reformulates and extends the new, group theoretic, mobility criterion recently developed by the authors, (, and , 2003, ASME J. Mech. Des., 125, pp. 70–80). In contrast to the Kutzbach-Grübler criterion, the new mobility criterion and the approach presented apply to a large class of single-loop overconstrained linkages. The criterion is reformulated, in terms of the well-known Jacobian matrices, for exceptional linkages and extended to linkages with partitioned mobility and trivial linkages. Several examples are included.