Determination of joint reaction forces in a symbolic form in rigid multibody systems

2011 ◽  
Vol 46 (11) ◽  
pp. 1796-1810 ◽  
Author(s):  
Slaviša Šalinić
Keyword(s):  
Multibody Systems ◽  
Symbolic Form ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Rigid Multibody Systems ◽  
Rigid Multibody ◽  
Joint Reaction

Analysis of Constraint Forces in Multibody Systems Based on the Differential Null Space Matrix Method

2019 ◽  
Author(s):  
Keisuke Kamiya
Keyword(s):  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Null Space ◽  
Governing Equations ◽  
Constraint Forces ◽  
Numerical Examples ◽  
Space Matrix ◽  
Rigid Multibody Systems ◽  
Rigid Multibody

Abstract This paper treats a problem to determine constraint forces in rigid mutibody systems. One of the most often applied algorithms for determination of constraint forces is based on the use of recursive Newton-Euler formalism. Another algorithm often applied for determination of constraint forces is based on the use of Lagrange multipliers. This paper presents a new method to determine constraint forces in rigid multibody systems. First relative displacements which violate the constraints, called anti-constraint relative displacements, are introduced, and governing equations which involve the constraint forces explicitly are derived. In the derived equations, the constraint forces appear independently from the Lagrange multipliers. Then, a method is proposed to determine the constraint forces by eliminating the Lagrange multipliers based on the methods proposed in previous papers by the author. The method is extended to have ability to treat systems with redundant constraints. Finally, validity of the proposed method is confirmed via numerical examples.

Elimination of Redundant Cut Joint Constraints for Multibody System Models

2003 ◽  
Vol 126 (3) ◽  
pp. 488-494 ◽  
Author(s):  
A. Mu¨ller
Keyword(s):  
Multibody Systems ◽  
Computational Effort ◽  
Basis Matrix ◽  
Constraint Equations ◽  
Kinematic Loops ◽  
Joint Constraints ◽  
Rigid Multibody Systems ◽  
Kinematic Loop ◽  
Rigid Multibody

The problem of dependent cut joint constraints for kinematic loops in rigid multibody systems is addressed. The constraints are reduced taking into account the subalgebra generated by the screw system of the kinematic loop. The elimination of dependent constraint equations is based on constructing a basis matrix of the screw algebra generated by loop’s screw system. This matrix is configuration independent and thus always valid. The determination of the sufficient constraints is achieved with a SVD or QR decomposition of this matrix. Unlike all other proposed approaches the presented method is singularity consistent because it is not the Jacobian which is decomposed, but instead a basis matrix for the loop algebra. Since this basis is obtained after a finite number of cross products the computational effort is negligible. Furthermore, because the elimination process is only necessary once in advance of the integration/simulation process, it proved valuable even if it does not remove all dependent constraints, as for paradoxical mechanisms.

scholarly journals Minimization of dynamic joint reaction forces of the 2-DOF serial manipulators based on interpolating polynomials and counterweights

2015 ◽  
Vol 42 (4) ◽  
pp. 249-260 ◽  
Author(s):  
Slavisa Salinic ◽  
Marina Boskovic ◽  
Radovan Bulatovic
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
Symbolic Form ◽  
Serial Manipulators ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Inertia Forces ◽  
Joint Reaction ◽  
Selection Of

This paper presents two ways for the minimization of joint reaction forces due to inertia forces (dynamic joint reaction forces) in a two degrees of freedom (2-DOF) planar serial manipulator. The first way is based on the optimal selection of the angular rotations laws of the manipulator links and the second one is by attaching counterweights to the manipulator links. The influence of the payload carrying by the manipulator on the dynamic joint reaction forces is also considered. The expressions for the joint reaction forces are obtained in a symbolic form by means of the Lagrange equations of motion. The inertial properties of the manipulator links are represented by dynamical equivalent systems of two point masses. The weighted sum of the root mean squares of the magnitudes of the dynamic joint reactions is used as an objective function. The effectiveness of the two ways mentioned is discussed.

Simple formulations of imposing moments and evaluating joint reaction forces for rigid-flexible multibody systems

2011 ◽  
Vol 69 (1-2) ◽  
pp. 127-147 ◽  
Author(s):  
Cheng Liu ◽  
Qiang Tian ◽  
Haiyan Hu ◽  
Daniel García-Vallejo
Keyword(s):  
Multibody Systems ◽  
Flexible Multibody Systems ◽  
Flexible Multibody ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Joint Reaction

Multiple impacts with friction in rigid multibody systems

1995 ◽  
Vol 7 (4) ◽  
pp. 471-497 ◽  
Author(s):  
Ch. Glocker ◽  
F. Pfeiffer
Keyword(s):  
Multibody Systems ◽  
Multiple Impacts ◽  
Rigid Multibody Systems ◽  
Rigid Multibody ◽  
Impacts With Friction
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