Analysis of multi-degree-of-freedom systems: Approximate and numerical methods

Abstract We study the performances of several numerical methods (Paoli-Schatzman, Newmark, Runge-Kutta) in order to compute periodic behavior of a simple one-degree-of-freedom impacting oscillator. Some theoretical results are given and numerical tests are performed. We compare mathematical and numerical results using our simple example exhibiting either finite or infinite number of impacts per period. Comparison of exact and numerical solution provides a practical order for each scheme. We conclude about the use of the different numerical methods.

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The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator

Journal of Mechanisms Transmissions and Automation in Design ◽

10.1115/1.3258901 ◽

1988 ◽

Vol 110 (1) ◽

pp. 35-41 ◽

Cited By ~ 331

Author(s):

C. Gosselin ◽

J. Angeles

Keyword(s):

Numerical Methods ◽

Parallel Manipulator ◽

Degree Of Freedom ◽

Design Criteria ◽

Algebraic Systems ◽

Kinematic Design ◽

Nonlinear Algebraic Systems ◽

Global Workspace ◽

Three Degree Of Freedom

In this paper, the design of a planar three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Four different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) the existence of a nonvanishing workspace for every orientation of the gripper (c) the maximization of the global workspace, and (d) the isotropy of the Jacobian of the manipulator. The four associated problems are formulated and their solutions are derived. Two of these require to resort to numerical methods for nonlinear algebraic systems. Results of optimum designs are also included.

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Analysis of single-degree-of-freedom systems: Approximate and numerical methods

Dynamics of Structures ◽

10.1201/b11772-15 ◽

2012 ◽

pp. 351-426

Keyword(s):

Numerical Methods ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree

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Operational Envelope of a Spatial Stewart Platform

Journal of Mechanical Design ◽

10.1115/1.2826256 ◽

1997 ◽

Vol 119 (2) ◽

pp. 330-332 ◽

Cited By ~ 17

Author(s):

F. A. Adkins ◽

E. J. Haug

Keyword(s):

Numerical Methods ◽

Driving Simulator ◽

Stewart Platform ◽

Degree Of Freedom ◽

Graphical Form ◽

Prior Work ◽

Unilateral Constraints ◽

Planar Mechanisms ◽

Operational Envelope ◽

Six Degree Of Freedom

This technical brief presents the operational envelope for the spatial Stewart platform and dome of a six degree of freedom driving simulator, extending prior work that has been limited to planar mechanisms and manipulators. The set of all points in space that can be occupied by any point in the dome of the simulator is defined as its operational envelope. The geometry of the driving simulator’s dome and unilateral constraints on actuator lengths are incorporated and details of the defining equations for the operational envelope are given. Numerical methods are used to calculate the boundary of the operational envelope and results are presented in graphical form.

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