Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 2—Velocity Transformation

1990 ◽  
Vol 112 (2) ◽  
pp. 160-167 ◽  
Author(s):  
C. W. Chang ◽  
A. A. Shabana
Keyword(s):  
Multibody Systems ◽  
Robot Manipulator ◽  
Spatial Dynamics ◽  
Dynamic Equations ◽  
Velocity Transformation ◽  
Joint Forces ◽  
Joint Coordinates ◽  
Deformable Bodies ◽  
Spatial System ◽  
Velocity Transformation Technique

In Part 1 of these two companion papers, the spatial system kinematic and dynamic equations are developed using the Cartesian and elastic coordinates in order to maintain the generality of the formulation. This allows introducing general forcing functions and adding and/or deleting kinematic constraints. In control applications, however, it is desirable to determine the joint forces associated with the joint variables. On the other hand the use of the joint coordinates to formulate the dynamic equations leads to a complex recursive formulation based on loop closure equations. In this paper a velocity transformation technique applicable to spatial multibody systems that consist of interconnected rigid and deformable bodies is developed. The Cartesian variables are expressed in terms of the joint and elastic variables. The resulting kinematic relationships are then employed to determine the joint forces associated with the joint variables. A spatial robot manipulator that manipulates an object is presented as a numerical example to exemplify the development presented in this paper.

An Efficient Dynamic Formulation for Solving Rigid and Flexible Multibody Systems Based on Semirecursive Method and Implicit Integration

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Francisco Javier Funes ◽  
Javier García de Jalón
Keyword(s):  
Multibody Systems ◽  
Dynamic Equations ◽  
Integration Process ◽  
Implicit Integration ◽  
Flexible Bodies ◽  
Velocity Transformation ◽  
Dynamic Formulation ◽  
Variable Stepsizes ◽  
Tangent Manifold ◽  
Stability Issues

This paper presents a method for solving the dynamic equations of multibody systems containing both rigid and flexible bodies. The proposed method uses independent coordinates and projects the dynamic equations on the constraint tangent manifold by means of a velocity transformation matrix. It can be used with a wide variety of integration formulae, considering both fixed and variable stepsizes. Topological semirecursive methods are used to take advantage of the relatively small number of parameters needed. An in depth implementation analysis is performed in order to evaluate the terms involved in the integration process. Numerical and stability issues are also discussed.

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.

Control Constraint Realization for Multibody Systems

2009 ◽  
Author(s):  
Alessandro Fumagalli ◽  
Pierangelo Masarati ◽  
Marco Morandini ◽  
Paolo Mantegazza
Keyword(s):  
Linear Systems ◽  
Multibody Systems ◽  
Matrix Pencil ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Control Constraint ◽  
Practical Observation ◽  
Alternative Condition ◽  
Deformable Bodies

This paper discusses the problem of control constraint realization applied to generic under-actuated multibody systems. The conditions for the realization are presented. Focus is placed on the tangent realization of the control constraint. An alternative condition is formulated, based on the practical observation that Differential-Algebraic Equations (DAE) need to be integrated using implicit algorithms, thus naturally leading to the solution of the problem in form of matrix pencil. The analogy with the representation of linear systems in Laplace’s domain is also discussed. The formulation is applied to the solution of simple, yet illustrative problems, related to rigid and deformable bodies. Some implications of considering deformable continua are addressed.

Allocation of Proximity Sensors for Obstacle Detection of a Robot Manipulator

1997 ◽  
Vol 9 (6) ◽  
pp. 482-489
Author(s):  
Takahiro Tsuchiya ◽  
◽  
Ryosuke Masuda ◽  
Keyword(s):  
Obstacle Avoidance ◽  
Robot Control ◽  
Robot Manipulator ◽  
Obstacle Detection ◽  
The Other ◽  
Work Space ◽  
Work Area ◽  
Joint Coordinates ◽  
Avoidance Control ◽  
Allocation Methods

In this paper, we discuss the sensor allocation problem in detecting obstacles in robot manipulators. The detection of obstacles in a work area is important for safety purposes and for the efficiency of robot control. Therefore, it is necessary to allocate the sensors properly on the links in a robot manipulator. Here, we propose two types of effective sensor allocation methods. One is based on the joint coordinates of the robot, and the other is based on the orthogonal work space. In addition, we show the allocation of additional sensors based on the quantitative conditions of the robot and its obstacles. The optical proximity sensor, which was developed by the authors, is used, and the proposed allocation methods are applied using a SCARA-type robot. It is proved, by experiments on obstacle avoidance control, that effective sensor allocations can be found.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Recursive Newton-Euler Dynamics and Sensitivity Analysis for Robot Manipulator With Revolute Joints

2020 ◽  
Author(s):  
Shuvrodeb Barman ◽  
Yujiang Xiang
Keyword(s):  
Robot Manipulator ◽  
Joint Torque ◽  
Planning Problem ◽  
Transformation Matrices ◽  
Revolute Joints ◽  
Sensitivity Equations ◽  
Joint Forces ◽  
Time Optimal ◽  
Planning Problems ◽  
Optimal Trajectory Planning

Abstract In this study, recursive Newton-Euler sensitivity equations are derived for robot manipulator motion planning problems. The dynamics and sensitivity equations depend on the 3 × 3 rotation matrices based on the moving coordinates. Compared to recursive Lagrangian formulation, which depends on 4 × 4 Denavit-Hartenberg (DH) transformation matrices, the moving coordinate formulation increases computational efficiency significantly as the number of matrix multiplications required for each optimization iteration is greatly reduced. A two-link manipulator time-optimal trajectory planning problem is solved using the proposed recursive Newton-Euler dynamics formulation. Only revolute joint is considered in the formulation. The predicted joint torque and trajectory are verified with the data in the literature. In addition, the optimal joint forces are retrieved from the optimization using recursive Newton-Euler dynamics.

Sign in / Sign up

Export Citation Format

Share Document