Bracing to Increase the Natural Frequency of a Manipulator: Analysis and Design

Abstract

The dynamic behavior of braced manipulators is analyzed. A braced manipulator is a manipulator that has been constrained by contact with the environment at a point other than the robot end effector, tool, or gripper. The analysis is restricted to manipulators with links that are rigid but joints that may be compliant. An expression is developed for the undamped natural frequency of an unbraced manipulator for small am plitudes of vibration. The kinematics of braced manipulators is described using admissible variables (i.e., variables that define the constrained admissible motion space), and the natural fre quency analysis is extended to braced manipulators. Dynamic analysis is used to design the ideal geometry of constraint to optimize the vibration characteristics of a robotic manipulator. It is shown that the lowest braced natural frequency is always greater than or equal to unbraced lowest natural frequency and thus can improve the dynamic performance of the robot. It is shown that there is a range of directions of bracing constraints that have the greatest effect in increasing the lowest natural frequency, and of this range it is possible to choose the most practically convenient. The results of the analysis and design are illustrated by their application to a grinding robot.

Get full access to this article

View all access options for this article.

References

Book, W.J. , and Sangveraphunsiri, V. 1984. Bracing strategy for robot operation. 1984 CISM-IFToMM/Ro. Man. Sy., pp. 179-185.

Delson, N. 1990. Design of bracing end effectors for dynamic advantage with application to robotic grinding. Master's thesis, Department of Mechanical Engineering, MIT.

Delson, N. , and West, H. 1990. Bracing to increase the natural frequency of a manipulator: Analysis and design. Japan-USA Symposium on Flexible Automation, Kyoto, Japan, pp. 19-26.

Eppinger, S.D. , and Seering, W.P. 1987. Understanding bandwidth limitations in robot force control . IEEE International Conference on Robotics and Automation, Raleigh, NC, pp. 904-909.

Guckenheimer, J. , and Holmes, P. 1983. Nonlinear Oscillation, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag .

Hollerbach, J.M. 1984. Dynamic scaling of manipulator trajectories. ASME J. Dynam. Sys. Control 106:102-106.

Mason, M.T. 1981. Compliance and force control for computer controlled manipulators . IEEE Trans. Sys. Man Cybernet. SMC-11 (June 6):418-432.

Ogata, K. 1970. Modern Control Engineering. Englewood Cliffs, NJ: Prentice-Hall.

Rivin, E.I. 1984. Effective rigidity of robot structures: Analysis and enhancement . Proc. American Control Conference, Boston, pp. 381-382.

10.

Rivin, E.I. 1988. Mechanical Design of Robots. New York : McGraw-Hill.

11.

Raibert, M.H. , and Craig, J.J. 1981. Hybrid position/force control of manipulators. J. Dynam. Sys. Measurement Control 102:126-133.

12.

Sharon, A. , Hogan, N. , and Hardt, D.E. 1988 (April 24-29). High bandwidth force regulation and inertia reduction using a macro/micro manipulator system. IEEE Conference on Robotics and Automation, Philadelphia , pp. 126-132.

13.

Strang, G. 1988. Linear Algebra and its Applications 3rd ed. New York: Academic Press .

14.

West, H. 1986. Kinematic analysis for the design and control of braced manipulators. Ph.D. thesis, Department of Mechanical Engineering , MIT.

15.

West, H. and Asada, H. 1985. Kinematic analysis and mechanical advantage of braced manipulators. Proc. ASME Winter Annual Meeting, Session on Robotics and Manufacturing Automation, Miami , pp. 175-186.

16.

Yoshikawa, T. 1987. Dynamic hybrid position/force control of robot manipulators—description of hand constraints and calculation of joint driving force. IEEE J. Robot. Automation RA-3(5):386-392.

17.

Zimmerman, M. , and West, H. 1990. Dynamics and sensor-based control of manipulators in contact with the environment. 1990 CISM-IFToMM/Ro. Man. Sy., Cracow, Poland, pp. 410-417.