A generalized algebraic formulation using instant centers (IC) was developed for the motion description of a general point in the rigid body under a planar 3-DOF (degrees-of-freedom) motion for up to the fifth order kinematics. This motion theory is being applied to planar wheeled mobile platforms. Though the first order and second order instant centers have been previously studied, the properties of higher order instant centers are yet to be understood. Also the expressions for third and higher order motion are highly coupled and more complex than the first and second order motion descriptions. To this effect, this paper studies some special case scenarios of planar rigid body motion that involve well documented 1-DOF motions such as a circle (cylinder /disk/wheel) rolling on a straight line (plane/flat, smooth surface), a circle rolling inside another circle, a circle rolling on another circle, etc. This study will help us understand the physical nature of the kinematic formulation using instant centers. Otherwise, numerical specifications for the higher order properties will have little known physical reference as to the meanings of their magnitudes.

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