# Rigid Link

^{th}DOF with respect to the global or a skew reference frame is:

For non-coincident nodes, no rigid body motion is possible.

A rigid link is equivalent to an infinitely stiff spring TYPE8.

A rigid link imposes the same velocity on all secondary nodes in one or more directions. The
directions are defined to a skew or global frame. Figure 1 displays a rigid link.

The velocity of the group of nodes rigidly linked together is computed using momentum
conservation (Section Definition, Equation 1). However, no global moment equilibrium
is respected.(1)

$${V}^{i}=\frac{{\displaystyle \sum _{i=i}^{N}{m}_{i}{v}_{i}}}{{\displaystyle \sum _{i=i}^{N}{m}_{i}}}$$

Angular velocity for the i^{th} DOF with respect to the global or a skew reference frame
is:(2)

$${\omega}^{i}=\frac{\left({\displaystyle \sum _{j=1}^{n}{I}_{j}^{i}{\omega}_{j}^{i}}\right)}{\left({\displaystyle \sum _{j=1}^{N}{I}_{j}^{i}}\right)}$$

For non-coincident nodes, no rigid body motion is possible.

A rigid link is equivalent to an infinitely stiff spring TYPE8.