A computer method for the dynamic analysis of a system of rigid bodies in plane motion

2004 ◽  
Vol 18 (2) ◽  
pp. 193-202
Author(s):  
Hazem Ali Attia
Keyword(s):  
Dynamic Analysis ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Computer Method ◽  
System Of Rigid Bodies

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.

Improving Techniques in Statically Equivalent Serial Chain Modeling for Center of Mass Estimation

2014 ◽  
Author(s):  
Bingjue Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Center Of Mass ◽  
Original System ◽  
Rigid Bodies ◽  
Joint Angles ◽  
Practical Applications ◽  
Serial Chain ◽  
System Of Rigid Bodies ◽  
Final Development ◽  
Data Error ◽  
Insight Into

Any articulated system of rigid bodies defines a Statically Equivalent Serial Chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. A SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed. Second, the problem of generating a SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.

On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

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.

The Geometry of Virtual Work Dynamics in Screw Space

1992 ◽  
Vol 59 (2) ◽  
pp. 411-417 ◽  
Author(s):  
Steven Peterson
Keyword(s):  
Tangent Space ◽  
Screw Theory ◽  
Virtual Work ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Coordinate Space ◽  
Dynamical Equations ◽  
Least Action ◽  
System Of Rigid Bodies ◽  
Configuration Manifold

In this paper, screw theory is employed to develop a method for generating the dynamic equations of a system of rigid bodies. Exterior algebra is used to derive the structure of screw space from projective three space (homogeneous coordinate space). The dynamic equation formulation method is derived from the parametric form of the principle of least action, and it is shown that a set of screws exist which serves as a basis for the tangent space of the configuration manifold. Equations generated using this technique are analogs of Hamilton’s dynamical equations. The freedom screws defining the manifold’s tangent space are determined from the contact geometry of the joint using the virtual coefficient, which is developed from the principle of virtual work. This results in a method that eliminates all differentiation operations required by other virtual work techniques, producing a formulation method based solely on the geometry of the system of rigid bodies. The procedure is applied to the derivation of the dynamic equations for the first three links of the Stanford manipulator.

scholarly journals Experimental Investigation of the Painlevé Paradox in a Robotic System

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Zhen Zhao ◽  
Caishan Liu ◽  
Wei Ma ◽  
Bin Chen
Keyword(s):  
Contact Point ◽  
Tangential Velocity ◽  
Rigid Bodies ◽  
Robotic System ◽  
Experimental Results ◽  
Painlevé Paradox ◽  
Dynamical Behaviors ◽  
Tangential Impact ◽  
System Of Rigid Bodies ◽  
Approach Zero

This paper aims at experimentally investigating the dynamical behaviors when a system of rigid bodies undergoes so-called paradoxical situations. An experimental setup corresponding to the analytical model presented in our prior work Liu et al. [2007, “The Bouncing Motion Appearing in a Robotic System With Unilateral Constraint,” Nonlinear Dyn., 49(1–2), 217–232] is developed, in which a two-link robotic system comes into contact with a moving rail. The experimental results show that a tangential impact exists at the contact point and takes a peculiar property that well coincides with the maximum dissipation principle stated in the work of Moreau [1988, “Unilateral Contact and Dry Friction in Finite Freedom Dynamics,” Nonsmooth Mechanics and Applications, Springer-Verlag, Vienna, pp. 1–82] the relative tangential velocity of the contact point must immediately approach zero once a Painlevé paradox occurs. After the tangential impact, a bouncing motion may be excited and is influenced by the speed of the moving rail. We adopt the tangential impact rule presented by Liu et al. to determine the postimpact velocities of the system, and use an event-driven algorithm to perform numerical simulations. The qualitative comparisons between the numerical and experimental results are carried out and show good agreements. This study not only presents an experimental support for the shock assumption related to the problem of the Painlevé paradox, but can also find its applications in better understanding the instability phenomena appearing in robotic systems.

The Mobility Equation and the Solvability of Joint Forces/Torques in Dynamic Analysis

1992 ◽  
Vol 114 (2) ◽  
pp. 257-262 ◽  
Author(s):  
Shin-Min Song ◽  
Xiaochun Gao
Keyword(s):  
Dynamic Analysis ◽  
Static Analysis ◽  
Rigid Bodies ◽  
Walking Machines ◽  
Spatial Mechanisms ◽  
Joint Forces ◽  
Simple Rules ◽  
Redundant Actuators

The mobility equation has been applied to predict the indeterminacy of unknown joint forces/torques in static analysis. In this paper, the mobility equation is modified to investigate the solvability of joint forces/torques of spatial mechanisms in dynamic analysis. Each factor which may contribute to indeterminacy is discussed and is explicitly expressed in the equation. With the modifications, the mobility equation can be applied to a system with or without redundant actuators. Together with the concept of subspaces and a few simple rules, the mobility equation can be used to identify the solvability of every joint unknown, as well as the equations which are required for the solutions, under the assumption of rigid bodies. This method can be used as a guidance of dynamic analysis in dealing with complicated systems such as walking machines and multi-fingered grippers.

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