A dynamic model for flexible manipulators with prismatic joints is presented in Part I of this study. Floating frames following a nominal rigid body motion are introduced to describe the kinematics of the flexible links. A Lagrangian approach is used in deriving the equations of motion. The work done by the rigid body axial force through the axial shortening of the link due to transverse deformations is included in the Lagrangian function. Kinematic constraint equations are used to describe the compatibility conditions associated with revolute joints and prismatic joints, and incorporated into the equations of motion by Lagrange multipliers. The small displacements due to the flexibility of the links are then discretized by a displacement based finite element method. Equations of motion are derived for the cases of prescribed rigid body motion as well as prescribed joint torques/forces through application of Lagrange’s equations. The equations of motion and the constraint equations result in a set of differential algebraic equations. A numerical procedure combining a constraint stabilization method and a Newmark direct integration scheme is then applied to obtain the system response. An example, previously treated in the literature, is presented to validate the modeling and solution methods used in this study.
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September 1990
Research Papers
Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints
Ye-Chen Pan,
Ye-Chen Pan
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109-2125
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R. A. Scott,
R. A. Scott
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109-2125
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A. Galip Ulsoy
A. Galip Ulsoy
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109-2125
Search for other works by this author on:
Ye-Chen Pan
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109-2125
R. A. Scott
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109-2125
A. Galip Ulsoy
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109-2125
J. Mech. Des. Sep 1990, 112(3): 307-314 (8 pages)
Published Online: September 1, 1990
Article history
Received:
August 1, 1988
Revised:
February 1, 1989
Online:
June 2, 2008
Citation
Pan, Y., Scott, R. A., and Ulsoy, A. G. (September 1, 1990). "Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints." ASME. J. Mech. Des. September 1990; 112(3): 307–314. https://doi.org/10.1115/1.2912609
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