New complex-number form of the cubic of stationary curvature in a computer-oriented treatment of planar path-curvature theory for higher-pair rolling contact

New complex number forms of the Euler-Savary Equation (ESE) for higher-pair rolling contact planar mechanisms were derived in a former paper by the authors.The present work, based on the former, deals with the derivation of the cubic of stationary curvature (CSC) in complex-vector form, suitable for digital computation.The CSC or Burmester’s circlepoint curve and its conjugate, the centerpoint curve for four infinitesimally close positions of the moving plane requires taking into account not only the curvature but also the rate of change of curvature of the rolling centrodes in the immediate vicinity of the position considered. The analytical procedure based on the theory developed in the present paper, when programmed for digital computation using complex arithmetic, takes care of the algebraic signs automatically, without the need for observing traditional sign conventions. The analysis is applicable to both higher-pair and lower-pair planar mechanisms. An example using the complex-number approach illustrates this.