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This paper presents a new matrix method for the kinematic analysis and the determination of the velocities, accelerations and jerks for planar mechanisms incorporating rolling, sliding, and pivoting members with a single or multiple degrees of freedom. It also presents a motion simulation procedure that uses the results of the kinematic analysis to estimate the successive positions of the members during the cycle of operation of the mechanism, with third order accuracy in time. Due to the improved accuracy, the proposed motion simulation procedure presents minimal member distortion caused by the accumulation of numerical errors, and does not require iterations for its convergence.