Perpetual points, in mathematics, were defined recently. In linear unforced flexible mechanical systems, they are associated with rigid body motion and form the perpetual manifolds. The concept of perpetual manifolds extended to the augmented perpetual manifolds for the externally forced flexible mechanical systems that are specific conditions they are moving as a rigid body. Herein using the concept of augmented perpetual manifolds and the conditions in obtaining rigid body motion the specifications that mechanical systems with linear and nonlinear ‘grounded’ springs and dashpots can admit rigid body motion are defined. More precisely, separating as external forces, these that are associated with linear and nonlinear springs and dashpots and using the conditions in obtaining the exact augmented perpetual manifolds the rigid body modes and motions analytically and numerically are shown. The classical theory of normal modes cannot directly predict this type of rigid body mode. The use of simple rules defining rigid body motion for mechanical systems is rather significant for the design of mechanical structures.