Kinematic Analysis of Planar Mechanisms

Here, we describe the method of projection of the vector contours of the mechanisms on the reference system axes and the method of the distances from geometry. The discontinuities that occur in the kinematic analysis of the mechanisms are shown, represented by the jump from one trigonometric quadrant to another. The nonlinear algebraic system of equations from the calculation of the mechanism positions have two equal values, one positive and the other negative, resulted from the square roots. Further on, the kinematic calculations (positions, velocities, and accelerations) are given for the driving links, for the moving linkages with planar motion and for the RRR, RRP, RPR, PRP, and RPP dyads. These rules are exemplified in detail on the slider-crank mechanism, giving relationships, diagrams, and successive positions of the mechanism. Finally, the kinematic analysis of the common triad is done with the matrix method.