Coupling Effect of A Flexible Link and A Flexible Joint

In this article the coupling effect of a flexible link and a flex ible joint is investigated. The system considered is a flexible link driven by an actuator through a flexible joint. First the dynamic equations of a flexible link-joint system are derived. Solutions of the system dynamic equations show that the fre quencies and mode shapes of the flexible link-joint system are parameterized in two ratios. One is the ratio of the moment of inertia of the link to that of the rotor of the actuator. The other is the ratio of the bending stiffness of the link to the torsion stiffness of the joint. Two important phenomena are discovered. The first is that in terms of the two ratios, there exist three regions of roots of the frequency equation—stiffening, softening, and mixed—and the coupling effect can be characterized by these three regions. The second is that the coupling effect can be reduced by appropriately choosing the combination of the two ratios. The results presented in the article are useful for design and control of flexible link-joint systems.

[1]  M. Vukobratovic,et al.  Scientific Fundamentals of Robotics 4: Real-Time Dynamics of Manipulation Robots , 1985 .

[2]  Veljko Potkonjak.  Contribution to the dynamics and control of robots having elastic transmissions , 1988, Robotica.

[3]  W. Book.  Recursive Lagrangian Dynamics of Flexible Manipulator Arms , 1984 .

[4]  Wayne J. Book,et al.  Modeling, design, and control of flexible manipulator arms: a tutorial review , 1990, 29th IEEE Conference on Decision and Control.

[5]  A. H. Soni,et al.  Coupling Effects of Kinematics and Flexibility in Manipulators , 1987 .

[6]  T. Bailey,et al.  Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam , 1985 .

[7]  H. Van Brussel,et al.  Discrete-Time Inverse Dynamics Control of Flexible Joint Robots , 1992 .

[8]  Eduardo Bayo,et al.  Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach , 1989, Int. J. Robotics Res..

[9]  Dong-Soo Kwon,et al.  An Inverse Dynamic Method Yielding Flexible Manipulator State Trajectories , 1990, 1990 American Control Conference.

[10]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[11]  Warren P. Seering,et al.  Using acausal shaping techniques to reduce robot vibration , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[12]  E. Barbieri,et al.  Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link , 1988, 1988 American Control Conference.

[13]  M. C. Readman,et al.  Stabilization of the Fast Modes of a Flexible-Joint Robot , 1992 .

[14]  Jean-Jacques E. Slotine,et al.  Robot analysis and control , 1988, Autom..

[15]  R. G. Fenton,et al.  Finite element analysis of high-speed flexible mechanisms , 1981 .

[16]  Anil K. Bajaj,et al.  Nonlinear Response of Flexible Robotic Manipulators Performing Repetitive Tasks , 1989 .

[17]  Mark W. Spong,et al.  Invariant manifolds and their application to robot manipulators with flexible joints , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[18]  Wayne J. Book,et al.  Feedback control of two beam, two joint systems with distributed flexibility , 1975 .

[19]  J.-H. Park,et al.  Integrated structure/control design of a two-link nonrigid robot arm for high-speed positioning , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[20]  H. Tokumaru,et al.  Inverse Dynamics of Flexible Robot Arms: Modeling and Computation for Trajectory Control , 1990 .

[21]  B. V. Chapnik,et al.  Modeling impact on a one-link flexible robotic arm , 1991, IEEE Trans. Robotics Autom..

[22]  Fengfeng Xi,et al.  A sequential integration method for inverse dynamic analysis of flexible link manipulators , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[23]  Wayne J. Book,et al.  Controller Design for Flexible, Distributed Parameter Mechanical Arms Via Combined State Space and Frequency Domain Techniques , 1983 .

[24]  Steven Dubowsky,et al.  On the Dynamic Analysis and Behavior of Industrial Robotic Manipulators With Elastic Members , 1983 .

[25]  Bruno Siciliano,et al.  A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators , 1988, Int. J. Robotics Res..

[26]  Ben Jonker,et al.  A Finite Element Dynamic Analysis of Flexible Manipulators , 1990, Int. J. Robotics Res..

[27]  W. Thomson.  Theory of vibration with applications , 1965 .

[28]  Giovanni Ulivi,et al.  Exact modeling of the flexible slewing link , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[29]  M. Spong.  Modeling and Control of Elastic Joint Robots , 1987 .

[30]  A. H. Soni,et al.  A generalized approach for forward and inverse dynamics of elastic manipulators , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[31]  Anthony Tzes,et al.  Application and Comparison of On-Line Identification Methods for Flexible Manipulator Control , 1991, Int. J. Robotics Res..

[32]  R. H. Cannon,et al.  Initial Experiments on the End-Point Control of a Flexible One-Link Robot , 1984 .