Domains of Interference Between Working Bodies in Mechanisms and Manipulators

1995 ◽  
Author(s):  
Edward J. Haug ◽  
Frederick A. Adkins ◽  
Chi-Mei Luh ◽  
Jia-Yi Wang
Keyword(s):  
Numerical Methods ◽  
Jacobian Matrix ◽  
Underlying Mechanism ◽  
Rank Deficiency ◽  
Ground Vehicle ◽  
Complementary Problems ◽  
Stewart Platforms ◽  
Working Bodies ◽  
Set Of Points

Abstract Criteria for the set of all points in a pair of working bodies in a mechanism or manipulator that can coincide for any kinematically admissible configuration of the underlying mechanism, called the domain of interference between the bodies, are formulated. Kinematic equations for the mechanism and parameterizations of the domains of the working bodies are used to derive analytical criteria for domains of interference. Three complementary problems are formulated and analyzed to characterize (1) the set of points in one of the interfering bodies that are occupied by any point in the second body, (2) the set of points in one of the interfering bodies that are occupied by any point on the boundary of the second body, and (3) the set of all points in space that are simultaneously occupied by points in the interfering bodies; each condition occurring for any kinematically admissible configuration of the mechanism. Analytical criteria for the boundaries of domains of interference for each of the three problems arc derived, based on row-rank deficiency of a sub-Jacobian matrix associated with the kinematic equations for each of the problems. Numerical methods for mapping boundaries of domains of interference are presented and illustrated for planar Stewart platforms with domes attached that are characteristic of flight or ground vehicle simulators.

Operational Envelopes for Working Bodies of Mechanisms and Manipulators

1995 ◽  
Author(s):  
Edward J. Haug ◽  
Frederick A. Adkins ◽  
Chi-Mei Luh
Keyword(s):  
Numerical Methods ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Kinematic Constraint ◽  
Rank Deficiency ◽  
Constraint Equations ◽  
Working Bodies ◽  
Operational Envelope ◽  
Three Dimensional Space

Abstract The set of all points in space that can be occupied by any point in the working body of a mechanism or manipulator is defined as its operational envelope. Criteria for points in and on the boundary of the operational envelope of working bodies with smooth boundaries are developed, for both parametric and equation representations of domains and boundaries of working bodies in two- or three-dimensional space. The criteria derived involve kinematic constraint equations for the underlying mechanism and equations that characterize the shape of the working body. A row rank deficiency condition is derived as a criterion for the boundary of the operational envelope, and numerical methods based on this condition for mapping the boundary are presented. An example involving a planar Stewart platform with a dome attached is analyzed numerically.

Novel use of the Monte-Carlo methods to visualize singularity configurations in serial manipulators

2021 ◽  
Vol 15 (2) ◽  
pp. 7948-7963
Author(s):  
Mohamed Aboelnasr ◽  
Hussein M Bahaa ◽  
Ossama Mokhiamar
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Curve Fitting ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Graphical Methods ◽  
Kinematic Singularity ◽  
Serial Manipulators ◽  
Serial Robots ◽  
Contour Plots

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

Workspace of a Gimbal With Joint Limits

1996 ◽  
Author(s):  
Har-Jou Yeh ◽  
Karim A. Abdel-Malek
Keyword(s):  
Degrees Of Freedom ◽  
Spherical Surface ◽  
Perturbation Technique ◽  
Underlying Mechanism ◽  
Singular Curve ◽  
Constraint Function ◽  
Rank Deficiency ◽  
Analytical Criterion ◽  
Joint Limits ◽  
Three Degrees Of Freedom

Abstract An analytical formulation for determining the workspace of a point on a body suspended in a Gimbal mechanism is presented. Although the gimbal mechanism comprises three degrees of freedom, the resulting workspace is a region on a spherical surface. The constraint function of the underlying mechanism is studied for singularities using a row-rank deficiency condition of its constraint Jacobian. Singular curves on the resultant spherical surface are determined by a similar analytical criterion imposed on the system’s subjacobian, to compute a set of two joint singularities. These singular curves define regions on the spherical surface that may or may not be accessible. A perturbation technique is then used to identify singular curve segments that are boundary to the workspace region. The methodology is illustrated through a numerical example.

Working Capability Analysis of Stewart Platforms

1996 ◽  
Vol 118 (2) ◽  
pp. 220-227 ◽  
Author(s):  
Chi-Mei Luh ◽  
F. A. Adkins ◽  
E. J. Haug ◽  
C. C. Qiu
Keyword(s):  
Numerical Methods ◽  
Motion Control ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Unilateral Constraints ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Capability Analysis ◽  
Working Capability ◽  
Stewart Platforms

Working capability analysis of planar and spatial Stewart platforms with unilateral constraints on actuator length is carried out using numerical methods based on analytical criteria for the boundary of the accessible output set. Restrictions on achievable motion at singular configurations associated with points interior to the accessible output set are also analyzed. Since movement of the working point on a spatial Stewart platform occurs in three-dimensional space, the boundary of the accessible output set is a two-dimensional surface. Numerical methods used in this analysis map one-dimensional solution sets, permitting the boundary of the accessible output set to be characterized by a family of one dimensional generators. Motion control restrictions inside the accessible output set are similarly characterized by families of interior singular curves, and barriers to motion control across surfaces defined are analyzed.

scholarly journals ANALYSIS OF THE EXISTING NUMERICAL METHODS FOR MODELING THE INTERACTION OF THE WORKING BODIES OF DIGGING AND SOIL-PROCESSING MACHINES WITH SOIL MEDIA

2020 ◽  
Vol 3 (3) ◽  
pp. 128-139
Author(s):  
Maksim Gnusov ◽  
Mihail Lisich
Keyword(s):  
Numerical Methods ◽  
Software Products ◽  
Modern Computer ◽  
Particle Hydrodynamics ◽  
Soil Media ◽  
Computational Fluid Dynamics Cfd ◽  
Working Bodies ◽  
Cfd Method ◽  
The Cost ◽  
Element Method

Carrying out theoretical studies of the working processes of various machines and units today has ample opportunities when using modern computer technologies. The use of programs greatly speeds up the study of complex systems under study. The use of simulation methods is advisable when the cost of carrying out real experimental research is high or, due to certain circumstances, making research on a real system impossible, and the calculation of the analytical model will allow many assumptions and approximations that will affect the entire system and change it. In the article, special attention is paid to the selection of the most suitable modeling method for studying the process, liquidation of a forest fire with a flow of soil, using serial software products. The analysis of existing numerical methods for modeling the interaction of working bodies of earth-moving and tillage machines with soil media is carried out. The studies performed by the discrete element method (DEM), the finite element method (FEM), the computational fluid dynamics (CFD) method, and the smooth particle hydrodynamics (SPH) method are analyzed. Conclusions are drawn on the prospects for the applicability of each of the methods for modeling the system of processes of processing and throwing soil.

scholarly journals Singularity analysis of the H4 robot using Grassmann–Cayley algebra

Robotica ◽  
2012 ◽  
Vol 30 (7) ◽  
pp. 1109-1118 ◽  
Author(s):  
Semaan Amine ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Daniel Kanaan
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Analysis Method ◽  
Rank Deficiency ◽  
Constraint Analysis ◽  
Cayley Algebra ◽  
Lower Mobility ◽  
Grassmann Cayley Algebra

SUMMARYThis paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using Grassmann–Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the H4 robot. All the parallel singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.

Operational Envelopes for Working Bodies of Mechanisms and Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 84-91 ◽  
Author(s):  
E. J. Haug ◽  
F. A. Adkins ◽  
Chi-Mei Luh
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Three Dimensions ◽  
Vehicle Suspension ◽  
Kinematic Constraint ◽  
Working Bodies ◽  
Operational Envelope ◽  
Vehicle Suspension System ◽  
Three Dimensional Space

The set of all points in space that are occupied by points in the working body of a mechanism or manipulator, for some kinematically admissible configuration, is defined as its operational envelope. Criteria for points on the boundary of the operational envelope of working bodies with smooth boundaries are developed, for both parametric and equation representations of domains and boundaries of working bodies, in two-and three-dimensional space. The criteria derived involve kinematic constraint equations for the underlying mechanism and equations that characterize the shape of the working body. A row rank deficiency condition is derived as a criterion for the boundary of the operational envelope, and numerical methods based on this condition for mapping the boundary are presented. Examples involving a planar Stewart platform with a dome attached and the wheel assembly of a vehicle suspension system in three dimensions are analyzed numerically.

Bifurcation Analysis of Charged Particles Moving on a Rough Surface Under Different Damping Effects

2017 ◽  
Vol 27 (05) ◽  
pp. 1750069
Author(s):  
Hao Zhang ◽  
Pengcheng Luo ◽  
Huifang Ding
Keyword(s):  
Rough Surface ◽  
Jacobian Matrix ◽  
Particle System ◽  
Charged Particles ◽  
Period Doubling ◽  
Dynamical Evolution ◽  
Underlying Mechanism ◽  
Damping Force ◽  
Damping Effects ◽  
The Stability

This paper deals with two types of bifurcation behaviors of charged particles moving on rough surface under different damping effects. Based on the derived models, the stability of the particle system is judged by eigenvalue analysis and then the eigenvalue movement of the Jacobian matrix is analyzed to reveal the underlying mechanism of the dynamical evolution. It is shown that in the particle system with constant damping force, the system loses stability via Neimark–Sacker bifurcation, whereas in the system with time-dependent damping force, the stability is lost by way of period-doubling bifurcation. In addition, a powerful tool called manifold is employed to meticulously characterize the phase space so as to clearly describe the process of energy evolution, which leads to the inherent understanding of the complex behaviors and particularly the global dynamical properties in the particle system. Finally, some bifurcation diagrams are obtained to give a more evident explanation of complex behaviors. These results are very useful for the entire transport knowledge of charged particle system.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai ◽  
Darwin G. Caldwell
Keyword(s):  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Rank Deficiency ◽  
Actuation Redundancy ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Lower Mobility

This paper investigates the behavior of a type of parallel mechanisms with a central strut. The mechanism is of lower mobility, redundantly actuated, and used for sprained ankle rehabilitation. Singularity and dexterity are investigated for this type of parallel mechanisms based on the Jacobian matrix in terms of rank deficiency and condition number, throughout the workspace. The nonredundant cases with three and two limbs are compared with the redundantly actuated case with three limbs. The analysis demonstrates the advantage of introducing the actuation redundancy to eliminate singularities and to improve dexterity and justifies the choice of the presented mechanism for ankle rehabilitation.

scholarly journals Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates

2021 ◽  
Vol 11 (1) ◽  
pp. 111-121
Author(s):  
G. Panou ◽  
R. Korakitis
Keyword(s):  
Numerical Methods ◽  
Analytical Method ◽  
Oblate Spheroid ◽  
Comparative Assessment ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
The Earth ◽  
Ellipsoidal Coordinates ◽  
Set Of Points ◽  
Exact Analytical Method

Abstract In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the Earth. Then, a theoretical and a numerical comparative assessment of the four methods is made. Furthermore, the new exact analytical method is applied for an almost oblate spheroid and for the case of the Moon and the results are compared. We conclude that, the generalized Panou and Korakitis’ numerical method, starting with approximate values from the new exact analytical method, is the best choice in terms of accuracy of the resulting ellipsoidal coordinates.

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