Automatic Formulation of Dynamic Equations of Motion of Robot Manipulators

1988 ◽  
Vol 202 (6) ◽  
pp. 397-404 ◽  
Author(s):  
D Pan ◽  
R S Sharp
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Chain Structure ◽  
Algebraic Manipulation ◽  
Dynamic Equations ◽  
Open Chain ◽  
Scalar Form ◽  
Memory Space ◽  
Manipulation Language

Based on the use of homogeneous transformation matrices with Denavit-Hartenberg notation and the Lagrangian formulation method, a general computer program ROBDYN.RED for the symbolic derivation of dynamic equations of motion for robot manipulators has been developed and is discussed in this paper. The program is developed by using REDUCE, an algebraic manipulation language, and is versatile for open-chain structure robot manipulators with any number of degrees of freedom and with any combination of types of joint. Considerations are also given to saving computer memory space required for execution and to minimizing the runtime. Several examples are included to demonstrate the use of the program. Equations of motion in scalar form can be automatically transferred to FORTRAN format for later numerical simulations. The efficiency of the resulting equations in terms of numerical integration is also discussed and some further developments to improve the efficiency are suggested.

Analysis of Varying Natural Frequencies and Damping Ratios of a Sample Parallel Manipulator Throughout its Workspace Using Linearized Equations of Motion

2001 ◽  
Author(s):  
Kris Kozak ◽  
Imme Ebert-Uphoff ◽  
William Singhose
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Parallel Architecture ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Dynamic Equations ◽  
Extreme Variation

Abstract This article investigates the dynamic properties of robotic manipulators of parallel architecture. In particular, the dependency of the dynamic equations on the manipulator’s configuration within the workspace is analyzed. The proposed approach is to linearize the dynamic equations locally throughout the workspace and to plot the corresponding natural frequencies and damping ratios. While the results are only applicable for small velocities of the manipulator, they present a first step towards the classification of the nonlinear dynamics of parallel manipulators. The method is applied to a sample manipulator with two degrees-of-freedom. The corresponding numerical results demonstrate the extreme variation of its natural frequencies and damping ratios throughout the workspace.

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.

A New Lagrangian Formulation of Dynamics for Robot Manipulators

1989 ◽  
Vol 111 (4) ◽  
pp. 559-566 ◽  
Author(s):  
Chang-Jin Li
Keyword(s):  
Control System ◽  
Dynamic Simulation ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Lagrangian Formulation ◽  
Lagrangian Dynamics ◽  
Highly Nonlinear ◽  
Mathematical Operations

In this paper, a new Lagrangian formulation of dynamics for robot manipulators is developed. The formulation results in well structured form equations of motion for robot manipulators. The equations are an explicit set of closed form second order highly nonlinear and coupling differential equations, which can be used for both the design of the control system (or dynamic simulation) and the computation of the joint generalized forces/torques. The mathematical operations of the formulation are so few that it is possible to realize the computation of the Lagrangian dynamics for robot manipulators in real-time on a micro/mini-computer. For a robot manipulator with n degrees-of-freedom, the number of operations of the formulation is at most (6n2 + 107n − 81) multiplications and (4n2 + 102n − 86) additions; for n = 6, about 780 multiplications and 670 additions.

Dynamic Analysis of a Multi-Rigid-Body Open-Chain System

1983 ◽  
Vol 105 (1) ◽  
pp. 28-34 ◽  
Author(s):  
G. R. Pennock ◽  
A. T. Yang
Keyword(s):  
Rigid Body ◽  
Robot Manipulators ◽  
Dynamic Equations ◽  
Newtonian Mechanics ◽  
Open Chain ◽  
Analytical Technique ◽  
Chain System ◽  
Joint Forces ◽  
Reaction Forces ◽  
Common Effort

In this paper we present an analytical technique, based on Newtonian mechanics with screw calculus and dual-number matrices, to derive the dynamic equations of a multi-rigid-body open-chain system. Next, we outline a systematic procedure to derive closed-form expressions for the joint forces and torques and the reaction forces and moments exerted on each member in the system. Finally, we illustrate the procedure with two examples of robot manipulators. It is hoped that the analytical technique presented here will provide a meaningful alternative, or serve as a complement to existing methods, in our common effort to advance the design of robot manipulators.

Automated Symbolic Derivation of Dynamic Equations of Motion for Robotic Manipulators

1986 ◽  
Vol 108 (3) ◽  
pp. 172-179 ◽  
Author(s):  
M. C. Leu ◽  
N. Hemati
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Dynamic Equations ◽  
Computer Memory ◽  
Symbolic Language ◽  
Symbolic Form ◽  
General Computer Program ◽  
Lagrange Formalism ◽  
General Computer

A general computer program for deriving the dynamic equations of motion for robotic manipulators using the symbolic language MACSYMA has been developed. The program, developed based on the Lagrange formalism, is applicable to manipulators of any number of degrees of freedom. Examples are given to illustrate how to use this program for dynamic equation generation. Advantages of expanding the dynamic equations into symbolic form are presented. Techniques for improving efficiency of equation generation, overcoming computer memory limitation, and approximating manipulator dynamics are discussed.

Design and Development of H∞ and μ-Synthesis Controllers for Nanorobotic Manipulation and Grasping Applications

2007 ◽  
Author(s):  
Reza Saeidpourazar ◽  
Beshah Ayalew ◽  
Nader Jalili
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Robust Controller ◽  
Accuracy And Precision ◽  
Highly Nonlinear ◽  
Linearized Model ◽  
High Level ◽  
Robust Controller Design

This paper presents the development of H∞ and μ-synthesis robust controllers for nanorobotic manipulation and grasping applications. Here a 3 DOF (Degrees Of Freedom) nanomanipulator with RRP (Revolute Revolute Prismatic) actuator arrangement is considered for nanomanipulation purposes. Due to the sophisticated complexity, and expected high level of accuracy and precision (of the order of 10−7 rad in revolute actuators and 0.25 nm in the prismatic actuator) of the nanomanipulator, there is a need to design a suitable controller to guarantee an accurate manipulation process. However, structure of the nanomanipulator employed here, namely MM3A, is such that the dynamic equations of motion of the nanomanipulator are highly nonlinear and complicated. Linearizing these dynamic equations of the nanomanipulator simplifies the controller design process significantly. However, linearization could suppress some critical information about the system dynamics. In order to achieve the precise motion of the nanomanipulator utilizing the simple linearized model, H∞ and μ-synthesis robust controller design approaches are proposed. Following the development of the controllers, numerical simulations of the proposed controllers on the nanomanipulator are used to verify the positioning performance.

scholarly journals Modular Multibody Formulation for Simulating Off-Road Tracked Vehicles

2014 ◽  
Vol 1 (2) ◽  
pp. 77 ◽  
Author(s):  
Mohamed A Omar
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Dynamic Equations ◽  
Solution Stability ◽  
Simulation Code ◽  
Tracked Vehicles ◽  
Main System ◽  
6 Degrees Of Freedom

This paper presents a formulation and procedure for incorporating the multibody dynamics analysis capability of tracked vehicles in large-scale multibody system.  The proposed self-contained modular approach could be interfaced to any exiting multibody simulation code without need to alter the existing solver architecture.  Each track is modeled as a super-component that can be treated separate from the main system.  The super-component can be efficiently used in parallel processing environment to reduce the simulation time.  In the super-component, each track-link is modeled as separate body with full 6 degrees of freedom (DoF).  To improve the solution stability and efficiency, the joints between track links are modeled as complaint connection.  The spatial algebra operator is used to express the motion quantities and develop the link’s nonlinear kinematic and dynamic equations of motion.  The super-component interacts with the main system through contact forces between the track links and the driving sprocket, the support rollers and the idlers using self-contained force modules.  Also, the super-component models the interaction with the terrain through force module that is flexible to include different track-soil models, different terrain geometries, and different soil properties.  The interaction forces are expressed in the Cartesian system, applied to the link’s equation of motion and the corresponding bodies in the main system.  For sake of completeness, this paper presents dynamic equations of motion of the links as well as the main system formulated using joint coordinates approach.

Analysis of Planar Multilink Cable Driven Robots Using Internal Routing Scheme

2020 ◽  
Author(s):  
Vishal Ramadoss ◽  
Darwin Lau ◽  
Dimiter Zlatanov ◽  
Matteo Zoppi
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Chain Structure ◽  
Kinematic Structure ◽  
Open Chain ◽  
Routing Scheme ◽  
Serial Chain ◽  
Minimum Number ◽  
Moving Platform ◽  
Cable Forces

Abstract The multilink cable driven robot (MCDR) is an extension of the cable robots where the moving platform is replaced by a multibody chain. It is typically an open-chain structure with multiple links and complex cable routing. This design introduces the advantages of having a serial kinematic structure and preserves the benefits associated with cable-driven parallel mechanism. To achieve a minimum number of actuating cables while possessing a large workspace region, a novel internal cable routing scheme is proposed. It is shown that by incorporating internal routing with multi-segment cables, any serial chain with n degrees of freedom can be controlled with n + 1 cables. In this work, through studying the kinematics and statics, we demonstrate how internally-routed cable actuation of multilink manipulators have an increased workspace and reduced cable forces to execute trajectories.

Sign in / Sign up

Export Citation Format

Share Document