Impact dynamics of multibody systems with frictional contact using joint coordinates and canonical equations of motion

1996 ◽  
Vol 9 (1-2) ◽  
pp. 53-71 ◽  
Author(s):  
M. Seabra Pereira ◽  
P. Nikravesh
Keyword(s):  
Multibody Systems ◽  
Frictional Contact ◽  
Equations Of Motion ◽  
Impact Dynamics ◽  
Dynamics Of Multibody Systems ◽  
Joint Coordinates

Modeling and Simulation of Assembly in a Free-floating Work Environment by a Free-floating Robot

1996 ◽  
Vol 118 (1) ◽  
pp. 115-120 ◽  
Author(s):  
S. K. Agrawal ◽  
M. Y. Chen ◽  
M. Annapragada
Keyword(s):  
Angular Momentum ◽  
Work Environment ◽  
Multibody Systems ◽  
Rigid Body Dynamics ◽  
Analytical Models ◽  
Impact Dynamics ◽  
Dynamics Of Multibody Systems ◽  
Body Dynamics ◽  
Freely Moving ◽  
Self Motion

Freely moving systems in space conserve linear and angular momentum. As moving systems collide, the velocities get altered due to transfer of momentum. The development of strategies for assembly in a free-floating work environment requires a good understanding of primitives such as self motion of the robot, propulsion of the robot due to onboard thrusters, docking of the robot, retrieval of an object from a collection of objects, and release of an object in an object pool. The analytics of such assemblies involves not only kinematics and rigid body dynamics but also collision and impact dynamics of multibody systems. This paper presents analytical models of assembly, built from the models of primitives, and some possible strategies for overall assembly.

Modeling a Robot With Flexible Joints and Decoupling its Equations of Motion

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Flexible Joints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Recent Advances ◽  
Dynamics Of Multibody Systems ◽  
Two Degree Of Freedom

Abstract Recent advances in the study of dynamics of multibody systems indicate the need for decoupling of the equations of motion. In this paper, our efforts are focused on this issue, and we have tried to expand the existing methods for multi-rigid body systems to include systems with some kind of flexibility. In this regard, the equations of motion for a planar two-degree-of-freedom robot with flexible joints is carried out using Lagrange’s equations and Kane’s equations with congruency transformations. The method of decoupling the equations of motion using Kane’s equations with congruency transformations is presented. Finally, the results obtained from both methods are compared.

Dynamics of Multibody Systems With Known Configuration Changes

1991 ◽  
Vol 58 (1) ◽  
pp. 215-221 ◽  
Author(s):  
J. J. McPhee ◽  
R. N. Dubey
Keyword(s):  
Numerical Simulation ◽  
Computer Program ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Rotation Vector ◽  
Dynamic Effects ◽  
Physical Systems ◽  
Dynamics Of Multibody Systems ◽  
Configuration Changes

The equations of motion are derived for a system with inertial properties that are varying in time as a result of known relative motions between the rigid bodies comprising the system. This vector-dyadic formulation has been encoded into a computer program, making use of the conformal rotation vector for the representation of rotations. The numerical simulation of two different physical systems is presented in order to illustrate the dynamic effects of the changing inertial properties, and the usefulness of the encoded formulation for modeling these effects.

A General Approach to the Dynamics of Nonholonomic Mobile Manipulator Systems

2002 ◽  
Vol 124 (4) ◽  
pp. 512-521 ◽  
Author(s):  
Qing Yu ◽  
I-Ming Chen
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Mobile Platform ◽  
Mobile Manipulator ◽  
Dynamic Interactions ◽  
Dynamics Of Multibody Systems ◽  
Minimum Number ◽  
Simulation And Control ◽  
And Control

This paper studies the dynamic modeling of a nonholonomic mobile manipulator that consists of a multi-degree of freedom serial manipulator and an autonomous wheeled mobile platform. The manipulator is rigidly mounted on the mobile platform, and the wheeled mobile platform moves on the ground subjected to nonholonomic constraints. Forward Recursive Formulation for the dynamics of multibody systems is employed to obtain the governing equation of the mobile manipulator system. The approach fully utilizes the existing equations of motion of the manipulator and that of the mobile platform. Furthermore, terms representing the dynamic interactions between the manipulator and the mobile platform can be observed. The resulting dynamic equation of the mobile manipulator has the minimum number of generalized coordinates and can be used for the purpose of dynamic simulation and control design, etc. The implementation issues of the model are discussed.

Direct and Adjoint Sensitivity Analysis of Multibody Systems Using Maggi’s Equations

2013 ◽  
Author(s):  
Daniel Dopico ◽  
Yitao Zhu ◽  
Adrian Sandu ◽  
Corina Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Third Party ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Dynamics Of Multibody Systems ◽  
Dynamical Optimization ◽  
Analytical Expressions ◽  
Coordinate Partitioning

The importance of the sensitivity analysis of multibody systems for several applications is well known, concretely design optimization based on the dynamics of multibody systems usually requires the sensitivity analysis of the equations of motion. A broad range of methods for the dynamics of multibody systems include the state space formulations based on Maggis equations, nullspace methods or coordinate partitioning. Dynamic sensitivities, when needed, are often calculated by means of finite differences but, depending of the number of parameters involved, this procedure can be very demanding in terms of CPU time and the accuracy obtained can be very poor in many cases. In this paper, several ways to perform the sensitivity analysis are explored and analytical expressions for the direct and adjoint sensitivity analysis of multibody systems are presented, all of them based on Maggi’s formulations. Moreover, two different approaches to the adjoint sensitivity analysis of multibody systems are presented. Although particularized to one formulation, the general expressions provided in the paper, are intended to be easily generalized and applied to any other formulation that can be expressed as an ODE-like system of equations, including penalty formulations. Besides, to check the validity and correctness of the proposed equations, the solutions of all the methods proposed are compared: 1) between them, 2) with the third party code FATODE and 3) with the numerical solution using real and complex perturbations. Finally, all the techniques proposed are applied to the dynamical optimization of a multibody system.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Dynamics of Multibody Systems With Spherical Clearance Joints

2005 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Contact Forces ◽  
Force Model ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Dynamics Of Multibody Systems ◽  
The Impact

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, being the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four bar mechanism is used as an illustrative example and some numerical results are presented, being the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops

1989 ◽  
Author(s):  
P. E. Nikravesh ◽  
G. Gim
Keyword(s):  
Equations Of Motion ◽  
Transformation Matrix ◽  
Velocity Transformation ◽  
Constraint Equations ◽  
Advantages And Disadvantages ◽  
Lagrange Multiplier Technique ◽  
Joint Coordinates ◽  
Minimum Number ◽  
Kinematic Loops ◽  
Equations Of Motions

Abstract This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

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