C. Lee et al., COORDINATE SYSTEM INDEPENDENT FORM OF INSTANTANEOUS INVARIANTS IN SPATIAL KINEMATICS, Journal of mechnical design, 115(4), 1993, pp. 946-952
This paper presents explicit equations for the instantaneous invariant
s 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 b
ased on information specifying the rigid body motion in any arbitrary
task coordinate systems. Explicit equations are presented for instanta
neous in variants up to the third order for spatial and spherical moti
ons and up to the fourth order for planar motions. The results provide
for a useful tool in design and analysis of mechanisms and motions ba
sed on instantaneous invariants. Examples are presented to illustrate
the theory.