Table 1 Displacement subgroups

{R(N, u)}

Revolute pair

Rotation about the axis determined by the unit vector u and point N

{T(v)}

Prismatic pair

Translation parallel to the unit vector v

{T(⊥u)}

Planar translation perpendicular to u

{T}

Three-dimensional translation in space

{G(u)}

Planar pair

Planar gliding motion determined by the normal vector u

{S(N)}

Spherical joint

Rotation about point N

{E}

Rigid connection, no relative motion

{D}

General spatial motion