ABSTRACT
This chapter looks at the constraint varieties of linkages from the viewpoint of mechanism science. Mechanism science is a rewarding field for many branches of applied mathematics. The chapter focuses on the algebraic and geometric aspects via Study parameters and dual quaternions. Mechanisms whose link graph have cycles are called parallel while mechanisms with linear link graph are called serial. Industrial specifications of mechanisms or robots require coordinate frames attached to each link. A mathematical description of a linkage and its possible configurations can be accomplished by translating the joint constraints into constraint equations. Fundamental concepts of algebraic geometry like "dimension," "singularity," or "prime decomposition" have a concrete kinematic meaning and are important in theoretical and applied mechanism science. Lower degree of freedom parallel manipulators draw attention in mechanism science. The reason is that for some tasks not the full six degrees of freedoms are required.
