Fibered incidence loops and kinematic loops

1987 ◽  
Vol 30 (2) ◽  
pp. 144-156 ◽  
Author(s):  
Elena Zizioli
Keyword(s):  
Kinematic Loops ◽  
Fibered Incidence

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.

scholarly journals Four-Pose Synthesis of Angle-Symmetric 6R Linkages

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Gábor Hegedüs ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
Rotation Angle ◽  
Dual Quaternions ◽  
Revolute Joints ◽  
Factorization Theory ◽  
Theory Of Motion ◽  
Kinematic Loops ◽  
Parametric Families ◽  
Synthesis Approach ◽  
Relative Motions

We use the recently introduced factorization theory of motion polynomials over the dual quaternions and cubic interpolation on quadrics for the synthesis of closed kinematic loops with six revolute joints that visit four prescribed poses. The resulting 6R linkages are special in the sense that the relative motions of all links are rational. They exhibit certain elegant properties such as symmetry in the rotation angles and, at least in theory, full-cycle mobility. Our synthesis approach admits either no solution or two one-parametric families of solutions. We suggest strategies for picking good solutions from these families. They ensure a fair coupler motion and optimize other linkage characteristics such as total rotation angle or linkage size. A comprehensive synthesis example is provided.

Orthogonal Complement-Based Divide and Conquer Algorithm: A Detailed Investigation of Its Performance

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Growth Rate ◽  
Arbitrary Number ◽  
Multibody Systems ◽  
Divide And Conquer ◽  
Orthogonal Complement ◽  
Error Growth ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Divide And Conquer Algorithm ◽  
Kinematic Loops

In this paper, we characterize the orthogonal complement-based divide-and-conquer (ODCA) [1] algorithm in terms of the constraint violation error growth rate and singularity handling capabilities. In addition, we present a new constraint stabilization method for the ODCA architecture. The proposed stabilization method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the performance of the ODCA with augmented [2] and reduction [3] methods. The results indicate that the performance of the ODCA falls between these two traditional techniques. Furthermore, using a numerical example, we demonstrate the effectiveness of the new stabilization scheme.

Computer Analysis of Machines With Planar Motion: Part 2—Dynamics

1970 ◽  
Vol 37 (3) ◽  
pp. 703-712 ◽  
Author(s):  
B. Paul ◽  
D. Krajcinovic
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Performance ◽  
Transient Behavior ◽  
Basic Program ◽  
Design Tool ◽  
Multiple Degrees Of Freedom ◽  
Kinematic Loops ◽  
Long Term Behavior ◽  
Made In

A uniform procedure is described for establishing the dynamic equation of motion for machines with single or multiple degrees of freedom. The procedure, which utilizes the independent kinematic loops of the machine, is readily programmed for a digital computer. The basic program is largely independent of the specific machine being analyzed and is capable of treating input forces, internal springs and dampers, all of which may depend nonlinearly upon position, velocity, or time. As an example, the dynamic performance of a Stirling cycle engine is analyzed without recourse to simplifying approximations usually made in engine analysis (i.e., constant crank speed, use of approximate “rotating” and “reciprocating” weights, neglect of higher harmonics in piston motion). It is shown that the method not only predicts transient behavior, but is capable of predicting steady (long-term) behavior without loss of accuracy, or excessive computer costs. The method described satisfies the major criteria of generality, accuracy, and economy, required of a truly practical design tool.

A Recursive Formulation for Real-Time Dynamic Simulation of Mechanical Systems

1991 ◽  
Vol 113 (2) ◽  
pp. 158-166 ◽  
Author(s):  
Dae-Sung Bae ◽  
Ruoh-Shih Hwang ◽  
Edward J. Haug
Keyword(s):  
Real Time ◽  
Dynamic Simulation ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Dynamic ◽  
Time Simulation ◽  
Kinematic Loops ◽  
Multi Body ◽  
Recursive Equations

A new recursive algorithm for real-time dynamic simulation of mechanical systems with closed kinematic loops is presented. State vector kinematic relations that represent translational and rotational motion are defined to simplify the formulation and to relieve computational burden. Recursive equations of motion are first derived for a single loop multi-body system. Faster than real-time performance is demonstrated for a closed loop manipulator, using an Alliant FX/8 multiprocessor. The algorithm is extended to multi-loop, multi-body systems for parallel processing real-time simulation in companion papers [1, 2] where performance of the algorithm on a shared memory multi-processor is compared with that achieved with other dynamic simulation algorithms.

scholarly journals Implementation of A Geometric Constraint Regularization For Multibody System Models

2014 ◽  
Vol 61 (2) ◽  
pp. 365-383 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Multibody System ◽  
Time Integration ◽  
Simulation Method ◽  
Dynamics Simulation ◽  
Computational Performance ◽  
Kinematic Loops ◽  
Computationally Expensive ◽  
Technical Systems ◽  
Loop Constraints

Abstract Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.

Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator

2004 ◽  
Vol 127 (4) ◽  
pp. 529-536 ◽  
Author(s):  
Waseem A. Khan ◽  
Venkat N. Krovi ◽  
Subir K. Saha ◽  
Jorge Angeles
Keyword(s):  
Mathematical Models ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Architecture ◽  
Robotic Systems ◽  
Orthogonal Complement ◽  
Recursive Algorithms ◽  
Planar Parallel Manipulator ◽  
Kinematic Loops

We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

A New Software Approach for the Simulation of Multibody Dynamics

2007 ◽  
Vol 2 (3) ◽  
pp. 274-278 ◽  
Author(s):  
Dmitry Vlasenko ◽  
Roland Kasper
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Design Tool ◽  
Design Engineers ◽  
Modular Software ◽  
The Matrix ◽  
Kinematic Loops ◽  
Virtual System ◽  
The Cost ◽  
Aided Design

This paper introduces a new modular software approach combining symbolical and numerical methods for the simulation of the dynamics of mechanical systems. It is based on an exact, noniterative object-oriented algorithm, which is applicable to mechanisms with any joint type and any topology, including branches and kinematic loops. The simulation of big well-partitioned systems has complexity O(N), where N is the total number of simulated bodies. A new design software Virtual System Designer (VSD) integrates this method with the three-dimensional computer aided design tool Autodesk Inventor, which minimizes the cost of the development of models and the training of design engineers. The most time-expensive routine of the simulation process in VSD is the calculation of the accelerations of each body, which needs to find the roots of matrix equations. Accounting for the sparsity of matrices can significantly improve the numerical efficiency of the routine. The preprocessing module, developed using Maple software, performs the symbolic simplification of the matrix multiplication’s and QR decomposition’s procedures. The new coordinate projection method is demonstrated. The results of the simulation of the dynamics of a double insulator chain example show the method’s stability and effectiveness.

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