Balancing of four-bar linkages using maximum recursive dynamic algorithm

This paper presents a simple, computationally efficient technique for the optimum balancing of four-bar linkages. The methodology is based on the maximum recursiveness of the dynamic equations for the evaluation of bearing forces. Besides, the balancing problem is posed as an optimum problem for which the optimality criteria and the constraints are formulated. Mass distribution of linkage is embedded in the constraints to obtain physically feasible linkage. The formulation is very generic and can be easily extended to multi-loop as well.

[1]  Edward John Routh,et al.  The elementary part of A treatise on the dynamics of a system of rigid bodies , 2009 .

[2]  Delbert Tesar,et al.  The theory of torque, shaking force, and shaking moment balancing of four link mechanisms , 1976 .

[3]  Ettore Pennestrì,et al.  Optimum balancing of four-bar linkages , 1991 .

[4]  V. Arakelian,et al.  Complete Shaking Force and Shaking Moment Balancing of Linkages , 1999 .

[5]  F R Tepper,et al.  The quantitative influence of complete force balancing on the forces and moments of certain families of four-bar linkages , 1974 .

[6]  H. Funabashi,et al.  On the Balancing of the Fluctuating Input Torques Caused by Inertia Forces in the Crank-and-Rocker Mechanisms , 1969 .

[7]  B. Roth,et al.  Momentum Balancing of Four-Bar Linkages , 1976 .

[8]  J. Angeles,et al.  The Formulation of Dynamical Equations of Holonomic Mechanical Systems Using a Natural Orthogonal Complement , 1988 .

[9]  G. G. Lowen,et al.  Theory of Shaking Moment Optimization of Force-Balanced Four-Bar Linkages , 1971 .

[10]  Subir Kumar Saha,et al.  Matrix Formulation of Constraint Wrenches for Serial Manipulators , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[11]  G. G. Lowen,et al.  A Novel Method for Prescribing the Maximum Shaking Force of a Four-Bar Linkage with Flexibility in Counterweight Design , 1983 .

[12]  G. G. Lowen,et al.  Determination of Force-Balanced Four-Bar Linkages With Optimum Shaking Moment Characteristics , 1971 .

[13]  Hong-Sen Yan,et al.  Kinematic and dynamic design of four-bar linkages by links counterweighing with variable input speed , 2001 .

[14]  M. Smith,et al.  Complete balancing of planar linkages by an equivalence method , 1994 .

[15]  A. A. Sherwood,et al.  The optimisation of mass distribution in mechanisms using dynamically similar systems , 1969 .

[16]  I. S. Kochev.  General theory of complete shaking moment balancing of planar linkages: a critical review , 2000 .

[17]  G. G. Lowen,et al.  Simultaneous Optimization of Dynamic Reactions of a Four-Bar Linkage With Prescribed Maximum Shaking Force , 1983 .

[18]  G. G. Lowen,et al.  Balancing of linkages—an update , 1983 .

[19]  P. Nikravesh.  Systematic reduction of multibody equations of motion to a minimal set , 1990 .

[20]  Parviz E. Nikravesh,et al.  Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops , 1989 .

[21]  S. Saha.  Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices , 1999 .

[22]  Parviz E. Nikravesh,et al.  Computer-aided analysis of mechanical systems , 1988 .

[23]  W. Carson,et al.  Feasible parameter design spaces for force and root-mean-square moment balancing an in-line 4R 4-bar synthesized for kinematic criteria , 1978 .

[24]  T. W. Lee,et al.  Optimum Balancing of Combined Shaking Force, Shaking Moment, and Torque Fluctuations in High-Speed Linkages , 1984 .

[25]  B. A Hockey.  The minimization of the fluctuation of input-shaft torque in plane mechanisms , 1972 .

[26]  R. S. Berkof,et al.  The input torque in linkages , 1979 .