Determination of Singularity-Free Zones in the Workspace of Planar 3-P̱RR Parallel Mechanisms

2006 ◽  
Vol 129 (6) ◽  
pp. 649-652 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Mathematical Derivation

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-P̱RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.

Analytic Determination of Wrench Closure Workspace of Spatial Cable Driven Parallel Mechanisms

2015 ◽  
Author(s):  
Zhiyu Sheng ◽  
Joon-Hyuk Park ◽  
Paul Stegall ◽  
Sunil K. Agrawal
Keyword(s):  
Simulation Study ◽  
Null Space ◽  
Boundary Surface ◽  
Parallel Mechanisms ◽  
Analytic Determination ◽  
Structure Matrix ◽  
Feasible Solutions

This paper proposes an efficient way of determining analytically the Wrench Closure Workspace (WCW) of spatial redundant cable-driven parallel mechanisms (CDPM). The method builds upon the boundary surface equations obtained from the null space of the structure matrix of CDPM. The set of feasible solutions is obtained that satisfies positive tension in the cables. This method was applied to characterize the WCW of spatial CDPM which has redundancy of 1 or 2. A simulation study was carried out to validate the accuracy and efficiency of the method. Several advantages over conventional approaches for determining the WCW were identified through simulation.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

A novel numerical approach for workspace determination of parallel mechanisms

2017 ◽  
Vol 31 (6) ◽  
pp. 3005-3015 ◽  
Author(s):  
Yiqun Zhou ◽  
Junchuan Niu ◽  
Zhihui Liu ◽  
Fuliang Zhang
Keyword(s):  
Numerical Approach ◽  
Parallel Mechanisms

Determination of Maximal Singularity-Free Workspace of Parallel Mechanisms Using Constructive Geometric Approach

2013 ◽  
pp. 307-314
Author(s):  
Mohammad Hadi Farzaneh Kaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Behnam Mashhadi Gholamali
Keyword(s):  
Geometric Approach ◽  
Parallel Mechanisms ◽  
Maximal Singularity

The Volume of Motion: Introduction, Derivation, and an Application Comparing Various Spinal Fixation Devices

1993 ◽  
Vol 115 (1) ◽  
pp. 43-46 ◽  
Author(s):  
J. J. Crisco
Keyword(s):  
Rigid Body ◽  
Three Dimensional ◽  
Spinal Fixation ◽  
Dimensional Parameter ◽  
Directional Information ◽  
One Dimensional ◽  
Fixation Devices ◽  
Spinal Fixation Devices ◽  
Mathematical Derivation

Range of motion (ROM), the displacement between two limits, is one of the most common parameters used to describe joint kinematics. The ROM is a one-dimensional parameter, although the motion at many normal and pathological joints is three-dimensional. Certainly, the ROM yields vital information, but an overall measure of the three-dimensional mobility at a joint may also be useful. The volume of motion (VOM) is such a measure. The translational VOM is the volume defined by all possible ROMs of a point on a rigid body. The rotational VOM, although its interpretation is not as tangible as the translational VOM, is a measure of the three-dimensional rotational mobility of a rigid body. The magnitude of the VOM is proportional to mobility; the VOM is a scaler, which does not contain any directional information. Experimental determination of the VOM is not practical since it would require applying loads in an infinite number of directions. The mathematical derivation given here allows the VOM to be calculated, with the assumption of conservative elasticity, from the resultant displacements of three distinct load vectors of equal magnitude. An example of the VOM is presented in the comparison of the biomechanical stabilizing potential of various spinal fixation devices.

Mathematical Solution for the Determination of Optimal Warehouse Location and Optimal Distribution Route

2005 ◽  
Author(s):  
Jagannadha Rao Naraparaju ◽  
Raghunandan A. Karamcheti ◽  
Z. Y. Wang
Keyword(s):  
Mathematical Models ◽  
Optimal Location ◽  
Optimal Routing ◽  
Practical Case ◽  
Transport Costs ◽  
Numerical Examples ◽  
Warehouse Location ◽  
Transportation Distance

In this paper, a procedure to determine the optimal location of a distribution warehouse, from which products are sent out to a group of companies has been studied. The goal was to minimize annual transportation distance between the warehouse and the customers. Fundamentals of mathematics have been used to formulate a virtual map showing the location of the present customers. Mathematical models and equations were developed making certain assumptions and an optimal location for the warehouse has been determined. Various factors that are involved in relocating the warehouse have been considered. Also a solution is given for the optimal location of a satellite or an auxiliary warehouse in addition to the existing one. A case study has been conducted on the model with the help of various numerical examples. Based on the optimal location of the relocated warehouse and the satellite warehouse obtained, the reductions in the transport costs were estimated. Once the optimal warehouse location has been found out, the next step was to find out an optimal route (least travel distance) for a practical case in which several companies have to be supplied with necessary products from one warehouse in a single trip. For this purpose, mathematical models were created and optimal routing algorithms were developed. Case studies have been conducted with the help of numerical examples. High amounts of savings in terms of travel distances, costs and time could be observed by the implementation of these algorithms.

Compliance Analysis of Mechanisms with Spatial Continuous Compliance in the Context of Screw Theory and Lie Groups

2010 ◽  
Vol 224 (11) ◽  
pp. 2493-2504 ◽  
Author(s):  
X Ding ◽  
J S Dai
Keyword(s):  
Case Studies ◽  
Lie Groups ◽  
Screw Theory ◽  
Elastic Beam ◽  
Parallel Mechanisms ◽  
Finite Segment ◽  
Numerical Examples ◽  
Spatial Compliance ◽  
Eigenvectors And Eigenvalues

This paper investigates the compliance effect on both serial and parallel mechanisms based on study of deflections of a finite segment of elastic beam with spatial compliance and applies eigenvectors and eigenvalues to identify principal screws in the mechanisms and parallel devices with spatial continuous compliance. With the analysis, compliance characteristics of both serial mechanisms and parallel devices can be identified with effect of compliance. Case studies are presented with numerical examples.

INVERSE ACOUSTIC SCATTERING PROBLEMS IN OCEAN ENVIRONMENTS

1999 ◽  
Vol 07 (02) ◽  
pp. 111-132 ◽  
Author(s):  
YONGZHI XU
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Stratified Medium ◽  
Computational Results ◽  
Scattering Problems ◽  
Numerical Examples ◽  
Layered Waveguide ◽  
Shape Determination

This paper presents theoretical and computational results from our research on inverse scattering problems for acoustic waves in ocean environments. In particular, we discuss the determination of a three-dimensional (3-D) distributed inhomogeneity in a two-layered waveguide from scattered sound and the shape determination of an object in a stratified medium. Numerical examples are presented.

Sign in / Sign up

Export Citation Format

Share Document