Systematic Use of Velocity and Acceleration Coefficients in the Kinematic Analysis of Single-DOF Planar Linkages

  • Raffaele Di GregorioEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


In single-degree-of-freedom (DOF) mechanisms, velocity coefficients (VCs) and their 1st derivative with respect to the generalized coordinate (acceleration coefficients (ACs)) only depend on the mechanism configuration. In addition, if the mechanism is a planar linkage, complex numbers are an easy-to-use tool for writing linkage’s loop equations that are formally differentiable. Here, both these results are combined to propose an algorithm that systematically uses VCs and ACs for solving the kinematic-analysis problems of single-DOF planar linkages. The proposed algorithm is efficient enough to be the kinematic block of any dynamic model of these linkages; also, it lends itself to present planar kinematics in graduate and/or undergraduate courses.


Planar Linkage Velocity Coefficient Acceleration Coefficient Higher Education 


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This work has been developed at the Laboratory of Advanced Mechanics (MECH-LAV) of Ferrara Technopole, supported by FAR2018 UNIFE funds and by Regione Emilia Romagna (District Councillorship for Productive Assets, Economic Development, Telematic Plan) POR-FESR 2007-2013, Attività I.1.1


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of FerraraFerraraItaly

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