Synthesis of Chebyshev Four-Bar Linkages and Analysis of Their Motion Properties via the Centrodes

The subject of this paper is the synthesis of Chebyshev four-bar linkages as three-poses rigid body guidance for obtaining an approximated long straight path of the coupler link midpoint. Moreover, the kinematic analysis of each type of the designed Chebyshev four-bar linkages is formulated in order to validate the proposed design procedure and to analyze the coupler rigid body motion by means of the centrodes, which take the form of approximated, circle and straight line (cycloidal motion) or internal circles (hypocycloidal motion) that tend to Cardan circles at infinity. Finally, applying the Roberts-Chebyshev theorem, the corresponding six-bar mechanisms are designed to obtain approximated long straight path parallel motions. Thus, implementing this formulation in Matlab, the proposed design procedure has been validated.