Assur group

In kinematics, an Assur group is a kinematic chain with zero degree of mobility, which added or subtracted from a mechanism do not alter its original number of degrees of freedom.

They have been first described by the Russian engineer Leonid Assur (1878–1920) in 1914.

Using an underscore "_" to indicate a guide following or preceding a slider in a translating (prismatic) joint, all possible dyadic isomers will be: RRR, RR_T, RRT_, RT_R, T_R_T, T_RT_, _TRT_, R_T_T, R_T_T, RT_T_, R_TT_ and RT__T.

Higher order Assur groups are known such as simple and multiple triads, simple and multiple thertad, pentad hexad etc.

When an Assur group is connected to the same link, zero degree-of-freedom entities known as Baranov trusses are obtained.

All possible Assur dyadic isomers (1), their simplified embodiment (2), and representative applications (3). [ 1 ]
Higher order Assur groups.