Research Papers

A Novel Dynamic Model for Single Degree-of-Freedom Planar Mechanisms Based on Instant Centers

[+] Author and Article Information
Raffaele Di Gregorio

Department of Engineering,
University of Ferrara,
Via Saragat, 1,
Ferrara 44122, Italy
e-mail: raffaele.digregorio@unife.it

1Corresponding author.

Manuscript received January 9, 2015; final manuscript received June 19, 2015; published online August 18, 2015. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 8(1), 011013 (Aug 18, 2015) (8 pages) Paper No: JMR-15-1006; doi: 10.1115/1.4030986 History: Received January 09, 2015

Many even complex machines employ single degree-of-freedom (single-dof) planar mechanisms. The instantaneous kinematics of planar mechanisms can be fully understood by analyzing where the instant centers (ICs) of the relative motions among mechanism’s links are located. ICs' positions depend only on the mechanism configuration in single-dof planar mechanisms and a number of algorithms that compute their location have been proposed in the literature. Once ICs positions are known, they can be exploited, for instance, to determine the velocity coefficients (VCs) of the mechanism and the virtual work of the external forces applied to mechanism's links. Here, these and other ICs' properties are used to build a novel dynamic model and an algorithm that solves the dynamic problems of single-dof planar mechanisms. Then, the proposed model and algorithm are applied to a case study.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Paul, B. , 1979, Kinematics and Dynamics of Planar Machinery, Prentice-Hall, Englewood Cliffs, NJ.
Gans, R. F. , 1991, Analytical Kinematics: Analysis and Synthesis of Planar Mechanisms, Butterworth-Heinemann, Boston, MA.
Butcher, E. A. , and Hartman, C. , 2005, “Efficient Enumeration and Hierarchical Classification of Planar Simple-Jointed Kinematic Chains: Application to 12- and 14-Bar Single Degree-of-Freedom Chains,” Mech. Mach. Theory, 40(9), pp. 1030–1050. [CrossRef]
Cardona, A. , and Pucheta, M. , 2007, “An Automated Method for Type Synthesis of Planar Linkages Based on a Constrained Subgraph Isomorphism Detection,” Multibody Syst. Dyn., 18(2), pp. 233–258. [CrossRef]
Murray, A. P. , Schmiedeler, J. P. , and Korte, B. M. , 2008, “Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms,” ASME J. Mech. Des., 130(3), p. 032302. [CrossRef]
Kong, X. , and Huang, C. , 2009, “Type Synthesis of Single-DOF Single-Loop Mechanisms With Two Operation Modes,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots (ReMAR 2009), London, June 22–24, pp. 136–141.
Barton, L. O. , 1993, Mechanism Analysis: Simplified Graphical and Analytical Techniques, 2nd ed., Marcel Dekker, New York.
Klein, A. W. , 1917, Kinematics of Machinery, McGraw-Hill, New York.
Foster, D. E. , and Pennock, G. R. , 2003, “A Graphical Method to Find the Secondary Instantaneous Centers of Zero Velocity for the Double Butterfly Linkage,” ASME J. Mech. Des., 125(2), pp. 268–274. [CrossRef]
Pennock, G. R. , and Kinzel, E. C. , 2004, “Path Curvature of the Single Flier Eight-Bar Linkage,” ASME J. Mech. Des., 126(3), pp. 470–477. [CrossRef]
Foster, D. E. , and Pennock, G. R. , 2005, “Graphical Methods to Locate the Secondary Instantaneous Centers of Single-Degree-of-Freedom Indeterminate Linkages,” ASME J. Mech. Des., 127(2), pp. 249–256. [CrossRef]
Yan, H.-S. , and Hsu, M.-H. , 1992, “An Analytical Method for Locating Instantaneous Velocity Centers,” 22nd ASME Biennial Mechanisms Conference, Scottsdale, AZ, Sept. 13–16, DE-Vol. 47, pp. 353–359.
Di Gregorio, R. , 2008, “An Algorithm for Analytically Calculating the Positions of the Secondary Instant Centers of Indeterminate Linkages,” ASME J. Mech. Des., 130(4), p. 042303. [CrossRef]
Wittenbauer, F. , 1923, Graphische Dynamik, Springer-Verlag, Berlin.
Eksergian, R. , 1928, “Dynamical Analysis of Machines,” Ph.D. dissertation, Clark University, Worcester, MA.
Angeles, J. , 1988, Rational Kinematics, Springer-Verlag, New York.
Wolfram, S. , 2003, The Mathematica Book, 5th ed., Wolfram Media, Witney, UK.
Nikravesh, P. E. , 2007, Planar Multibody Dynamics: Formulation, Programming, and Applications, CRC Press, Boca Raton, FL.
Roe, J. W. , 1926, English and American Tool Builders, McGraw-Hill, New York.


Grahic Jump Location
Fig. 1

Intersection of two lines, the IC Iij lies on: (a) the two lines are identified through the A–K theorem and (b) the two lines refer to either a slipping contact or a prismatic pair [13]

Grahic Jump Location
Fig. 2

Instantaneous relative motion between links j and i: (a) instantaneous rotation (Iji is a finite point of the motion plane; the motion is uniquely defined by Iji and θ·ji) and (b) instantaneous translation (Iji is the point at infinity of the lines perpendicular to the translation direction; the motion is uniquely defined by the translation velocity s·jitji)

Grahic Jump Location
Fig. 3

Generic scheme of a single-dof planar mechanism with m links (Gj, μj, and λj, for j = 2,…, m, are the center of mass, the mass, and the inertia moment about its center of mass, respectively, of the jth link)

Grahic Jump Location
Fig. 4

Link j loaded by the resultant torque, Mjk, about Gj and the resultant force, Rjfj, of all the active forces applied to it: (a) the link performs an instantaneous rotation about Ij1 and (b) the link performs an instantaneous translation parallel to tj1

Grahic Jump Location
Fig. 5

VCs as a function of θ21 (a1 = 0.2 m, a2 = 0.1 m, a4 = 0.4 m, a5 = 0.2 m, and a6 = 0.2 m): (a) ν3 and ν5 and (b) ν6

Grahic Jump Location
Fig. 6

The generalized inertia coefficient, J, (a) and its derivative with respect to θ21 (b) of the shaper mechanism with the geometry of Fig. 5 and the mass distribution data of Table 1 as a function of θ21

Grahic Jump Location
Fig. 7

Generalized inertia torque, τ, as a function of θ21 in the case θ·21 = 20 rpm, θ··21 = 0, and a cutting force of 500 N

Grahic Jump Location
Fig. 8

Link j: determination of Gj's position after the link pose, with respect to the frame, has been computed

Grahic Jump Location
Fig. 9

Shaper mechanism: kinematic scheme and notations




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In