Discriminant method for the mobility identification of single degree-of-freedom double-loop linkages

This paper presents the first successful attempt that extends the discriminant method to the mobility analysis of non-bimodal linkages. The singularity condition and the joint rotation space are expressed and identified by the discriminant functions. The method is algebraic and the discriminant function is derived based on the form of equations essential for the displacement analysis of the linkage. Therefore, its applicability is not restricted by the type of joints or the physical appearance of the linkage. It is applicable to any single degree-of-freedom planar and spherical double-loop linkages regardless the choice of the input, output, or fixed link. It is also applicable to spatial linkages with the similar displacement equation form. The method is ideal for automated mobility rectification and is demonstrated with single-DOF planar six-bar linkages.