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Abstract--Kinematic pairs in a spatial mechanism are viewed either as allowing relative screw motion between links or as constraining the motion of the two chains of the mechanism connected to the two elements of the pair. Using pair geometry constraints of the sphere-plane and sphere-groove kinematic pairs, the. Thus, a planar mechanism may be described with a simple drawing, and its analysis or synthesis may be carried out with the help of planar geometry. In the study of spatial mechanisms this ease of representation and visualization no longer exists. A description of spatial mech- anisms free of ambiguity requires a careful. Kinematics (cont.) open chain - a kinematic chain where one link (the unitary link) is connected to a single joint. Parallel chain - a mechanism with open or closed. Spatial Relationships. A free body has 6 spatial degrees of freedom: translations: t ∈ R. 3 rotations: R ∈ SO(3).