Dynamic Analysis of Mechanisms Using Constrained Lagrangian Bond Graphs

1992 ◽  
Author(s):  
Y. A. Khulief
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Bond Graph ◽  
Rigid Bodies ◽  
Interconnected System ◽  
Lagrangian Equations ◽  
System Of Rigid Bodies ◽  
Reaction Forces ◽  
Bond Graph Modeling ◽  
Generalized Constraint

Abstract A method for dynamic analysis of mechanisms using the Lagrangian equations of motion for an interconnected system of rigid bodies is presented. The method stems from a recent extension to the bond graph modeling technique. Intrinsically, this approach allows the formulation of the final form of equations for holonomic systems without recourse to the Lagrangian function. Consequently, the burdens of deriving the expressions for kinetic and potential energies, and performing the necessary differentiations have been eliminated. This method calls only for constructing the Jacobian matrix of constraints, and then employing a bond graph that accounts for the generalized constraint reaction forces.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

Formulation of the Equations of Motion of RRPR Robot Manipulator

2000 ◽  
Author(s):  
Hazem Ali Attia ◽  
Tarek M. A. El-Mistikawy ◽  
Adel A. Megahed
Keyword(s):  
Dynamic Analysis ◽  
Efficient Solution ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Second Law ◽  
Equivalent System ◽  
Constraint Forces ◽  
Dynamic Formulation ◽  
System Of Particles

Abstract In this paper the dynamic analysis of RRPR robot manipulator is presented. The equations of motion are formulated using a two-step transformation. Initially, a dynamically equivalent system of particles that replaces the rigid bodies is constructed and then Newton’s second law is applied to derive their equations of motion. The equations of motion are then transformed to the relative joint variables. Use of both Cartesian and joint variables produces an efficient set of equations without loss of generality. For open chains, this process automatically eliminates all of the non-working constraint forces and leads to an efficient solution and integration of the equations of motion. The results of the simulation indicate the simplicity and generality of the dynamic formulation.

Dynamic Analysis of Multi-Rigid-Body Systems

1974 ◽  
Vol 96 (3) ◽  
pp. 886-892 ◽  
Author(s):  
V. K. Gupta
Keyword(s):  
Digital Simulation ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Mechanism Analysis ◽  
Spatial Mechanism ◽  
Higher Derivatives ◽  
Reaction Forces ◽  
Representative Problem ◽  
Classical Vector ◽  
Vector Approach

A method is presented for formulating and solving the Newton-Euler equations of motion of a system of interconnected rigid bodies. The digital simulation may involve numerical integration of the kinematic equations as well as the dynamic equations. The reaction forces and torques resulting from rigid constraints imposed at the connecting joints are also determined. The derivation of kinematic expressions for first and higher derivatives is demonstrated based on direct differentiation of the rotation matrix in the spirit of the classical vector approach. A representative problem in spatial mechanism analysis is solved and illustrated with numerical results.

scholarly journals Energetically Consistent Calculations for Oblique Impact in Unbalanced Systems With Friction

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
W. J. Stronge
Keyword(s):  
Energy Dissipation ◽  
Equations Of Motion ◽  
Oblique Impact ◽  
Rigid Bodies ◽  
Contact Period ◽  
Analytical Mechanics ◽  
Normal Contact ◽  
System Of Rigid Bodies ◽  
Energy Gains ◽  
The Impact

Analytical mechanics is used to derive original 3D equations of motion that represent impact at a point in a system of rigid bodies. For oblique impact between rough bodies in an eccentric (unbalanced) configuration, these equations are used to compare the calculations of energy dissipation obtained using either the kinematic, the kinetic, or the energetic coefficient of restitution (COR); eN,eP, or e*. Examples demonstrate that for equal energy dissipation by nonfrictional sources, either eN≤e*≤eP or eP≤e*≤eN depending on whether the unbalance of the impact configuration is positive or negative relative to the initial direction of slip. Consequently, when friction brings initial slip to rest during the contact period, calculations that show energy gains from impact can result from either the kinematic or the kinetic COR. On the other hand, the energetic COR always correctly accounts for energy dissipation due to both hysteresis of the normal contact force and friction, i.e., it is energetically consistent.

Closed and Expanded Form of Manipulator Dynamics Using Lagrangian Approach

1985 ◽  
Vol 107 (2) ◽  
pp. 223-225 ◽  
Author(s):  
T. Wang ◽  
D. Kohli
Keyword(s):  
Equations Of Motion ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
Lagrangian Approach ◽  
Alternative Derivation ◽  
Manipulator Dynamics ◽  
Lagrangian Equations ◽  
A Chain ◽  
Expanded Form ◽  
Simplified Form

An alternative derivation of the equations of motion of a chain of rigid bodies using Lagrangian equations of motion is presented. In an effort to reduce the complexity of the coefficients appearing in the equations of motion, a modified form of Lagrangian equations due to Silver [3] are utilized. This approach leads to a simplified form of coefficients of the equation of motion.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies—Part 1: Characterization and Prediction of the Kinematic Constraint Changes

1991 ◽  
Vol 113 (1) ◽  
pp. 70-76 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part 1. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforessen changes in topology. Part 2 presents the implementation of the characterizations into a simulation strategy and presents examples.

scholarly journals A Two-Dimensional Discrete Model for Dynamic Analysis of Belt Transmission with Dry Friction

2014 ◽  
Vol 61 (4) ◽  
pp. 571-593
Author(s):  
Krzysztof Kubas
Keyword(s):  
Dynamic Analysis ◽  
Dry Friction ◽  
Discrete Model ◽  
Equations Of Motion ◽  
Friction Model ◽  
Rigid Bodies ◽  
Friction Forces ◽  
Calculation Results ◽  
Model Of Friction ◽  
Belt Transmission

Abstract The paper presents a model for dynamic analysis of belt transmission. A twodimensional discrete model was assumed of a belt consisting of rigid bodies joined by translational and torsion spring-damping elements. In the model, both a contact model and a dry friction model including creep were taken into consideration for belt-pulley interaction. A model with stiffness and damping between the contacting surfaces was used to describe the contact phenomenon, whereas a simplified model of friction was assumed. Motion of the transmission is triggered under the influence of torque loads applied on the pulleys. Equations of motion of separate elements of the belt and pulleys were solved numerically by using adaptive stepsize integration methods. Calculation results are presented of the reaction forces acting on the belt as well as contact and friction forces between the belt body and pulley in the sample of the belt transmission. These were obtained under the influence of the assumed drive and resistance torques.

A unified tensor approach to the analysis of mechanical systems

1997 ◽  
Vol 211 (4) ◽  
pp. 313-322 ◽  
Author(s):  
A A Fogarasy ◽  
M R Smith
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Equation Of Motion ◽  
Newtonian Mechanics ◽  
Kinematic Constraint ◽  
Lagrangian Equation ◽  
Generalized Coordinates ◽  
Lagrangian Equations

It is shown in this paper that all methods of dynamic analysis of mechanisms used in practice can be derived from an invariant formed from the Lagrangian equation of motion. For the dynamic analysis of mechanisms subjected to kinematic constraint conditions, the Lagrangian equations of motion are far more suitable than the Newtonian approach. Since the Lagrangian equations are tensor equations, they are valid irrespective of what kind of generalized coordinates are used. This is not so, however, when the Newtonian approach is used. It is demonstrated by a simple example that a careless use of Newtonian mechanics can lead to erroneous results.

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