The classical cardanic motion and the swinging-block linkage are basic planar mechanisms. In the following investigation, the objective is the analysis of their three-dimensional (and, hence, more versatile) counterparts: the skew slider-crank mechanism and the skew swinging-block linkage. These linkages as far as we are aware, have not yet been analyzed analytically. An analysis utilizing their algebraic geometry will be instructive in determining their displacements and derivatives in closed form. This, in turn, should be useful in facilitating three-dimensional applications.
With the ever-increasing sophistication in the area of mechanisms design and analysis, we believe that the time has come for the analysis of these linkages, including their algebraic geometry. This is the objective of this investigation.