This paper presents explicit equations for the instantaneous invariants of spatial kinematics that are coordinate systems independent. This eliminates the need for laborious coordinate transformations necessary in the determination of the canonical coordinate systems. It provides for a direct method for the calculation of instantaneous invariants based on information specifying the rigid body motion in any arbitrary task coordinate systems. Explicit equations are presented for instantaneous invariants up to the third order for spatial and spherical motions and up to the fourth order for planar motions. The results provide for a useful tool in design and analysis of mechanisms and motions based on instantaneous invariants. Examples are presented to illustrate the theory.

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