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.

Computational Analysis of Multibody Dynamic Systems Using Nonlinear Recursive Formulation

2009 ◽  
Vol 419-420 ◽  
pp. 289-292
Author(s):  
Yunn Lin Hwang ◽  
Shen Jenn Hwang ◽  
Zi Gui Huang ◽  
Ming Tzong Lin ◽  
Yen Chien Mao ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Recursive Formulation ◽  
Loosely Coupled ◽  
Multibody Dynamic ◽  
Joint Coordinates ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Strong Dynamic ◽  
Joint Reaction

. In this paper the computer implementation of the nonlinear recursive formulation in multibody dynamics systems is described. The organization of the computer algorithm which is used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute and joint coordinates is discussed. The inertia projection schemes used in most existing recursive formulations for the dynamic analysis of deformable mechanisms lead to dense coefficient matrices in the equations of motion. Consequently, there are strong dynamic couplings between the joint and elastic coordinates. By using the inertia matrix structure of deformable mechanical systems and the fact that the joint reaction forces associated with the elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent of the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as the joint reaction forces. The multibody flexible four-bar system is used as an example to demonstrate the use of the procedure discussed in this paper.

Mechanism Analysis Using Implicit Constraints

2008 ◽  
Author(s):  
George H. Sutherland
Keyword(s):  
Equations Of Motion ◽  
Reaction Force ◽  
Mechanism Analysis ◽  
Kinematic Parameters ◽  
Joint Reaction Force ◽  
Dynamic Mechanisms ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Mechanism Kinematic ◽  
Joint Reaction

This paper introduces an approach to kinematic and dynamic mechanisms analysis where one or more joints are modeled using joint component relative displacements that approximate real joint behavior. This approach allows for the simultaneous nonrecursive solution for both mechanism kinematic parameters and selected dynamic joint reaction forces. Also, for closed loop mechanisms, the approach eliminates the need for forming explicit loop closure constraint equations, so that the dynamic equations of motion, derived using either the Newtonian or Lagrangian method, have a simplified unconstrained form. The key element underlying the approach is the formation of axioms for the standard mechanism joint types that describe the form of the joint reaction force and/or moment in terms of a virtual (or real) displacement between the joint components.

Decoupling Methods in Flexible Multibody Dynamics

1993 ◽  
Author(s):  
Yunn-Lin Hwang
Keyword(s):  
Degrees Of Freedom ◽  
Sparse Matrix ◽  
Deformable Body ◽  
Recursive Methods ◽  
Coupled Equations ◽  
Flexible Multibody ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Modal Coordinates ◽  
Joint Reaction

Abstract The inertia projection schemes used in the existing recursive methods for the dynamic analysis of flexible multibody systems lead to dense coefficient matrices in the acceleration equations. Consequently, there is a strong dynamic coupling between the joint and modal coordinates. When the number of modal degrees of freedom increases, the size of the coefficient matrix in the acceleration equations becomes large and consequently the use of these recursive methods for solving the joint and modal accelerations becomes less efficient. This investigation discusses the problems associated with the inertia projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and modal accelerations using these methods requires the factorization of nonlinear matrices whose dimensions depend on the number of modal degrees of freedom of the system. An amalgamated formulation that can be used to decouple the modal and joint accelerations is proposed. In this amalgamated formulation, the relationships between the Cartesian, modal and joint variables and the generalized Newton-Euler equations are utilized to develop systems of loosely coupled equations that have sparse matrix structure. Using the structure of the inertia matrix of the deformable body and the fact that joint reaction forces associated with modal coordinates do not represent independent variables, a reduced system of equations whoSe dimension is independent of the number of modal degrees of freedom is obtained. This system can be solved for the joint accelerations as well as the joint reaction forces. The use of the procedure developed in this paper can be used for open-loop and closed-loop mechanical systems.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

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