ABSTRACT
In this chapter, the authors shall mainly discuss the methods for obtaining the displacement equation of three dimensional linkages. The degrees-of-freedom of a spatial linkage can be obtained (except in special cases with particular kinematic dimensions) by extending the Kutzbach equation discussed in the chapter. They saw that for some simple, (four-link) spatial linkages, the displacement equation can be obtained by using analytic geometry. The displacement analysis of a spatial linkage using the matrix method is based on following the closed loops existing in the linkage. They discusses the Grashof criterion for four-link planar linkages. The concept of dual numbers has been used profitably for displacement analysis of spatial mechanisms. If a mechanism cannot be assembled, the discreminant polynomial is negative for all values of the input variables when again, the roots of the discriminant polynomial will be non-real.
