An approach to the displacement analysis of spatial mechanisms—I : Principles and mechanisms with low degree equations

The use of direction cosines and projections is shown to be adequate and efficient for deriving the input-output displacement equations for spatial mechanisms, up to 6-link 5R-C mechanisms. The displacement equations are derived for several 5-link mechanisms and 6-link 4R-P-C mechanisms. These derivations are quick and direct and automatically avoid extraneous roots. The method of derivation for 6-link 5R-C mechanisms is indicated, showing how extraneous roots are avoided by the approach. Part I explains the method, applied to 5-link mechanisms that yield a 4th degree equation. Part II shows the application to 5- and 6-link mechanisms with equations of higher degree.