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.

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.

scholarly journals AN ANALYTICAL METHOD TO FIND WORKSPACE OF A ROBOTIC MANIPULATOR

1970 ◽  
Vol 41 (1) ◽  
pp. 25-30 ◽  
Author(s):  
Khushdeep Goyal ◽  
Davinder Sethi
Keyword(s):  
Analytical Method ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Singular Behavior ◽  
Singular Surfaces ◽  
Rank Deficiency ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
Robot Wrist ◽  
Three Dimensional Space

The workspace of a Robot is determined by an analytical method. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation for serial kinematic chains. This method is based upon analytical criteria for determining singular behavior of the mechanism. By manipulating the Jacobian of the robot by the row rank deficiency condition, the singularities are computed. Then these singularities are substituted into the constraint equations to parameterize singular surfaces. The boundary conditions of the joints are substituted to obtain the other set of singularities. These singularities are substituted in the wrist vector to obtain the range of motion of the robot wrist in three dimensional space, which is the workspace of the Robot. These singularities are plotted in Matlab to develop all the surfaces enveloping the workspace of the Robot. The priactical examples of RV-M1 MITSIBUSHI ROBOT and 3 DOF spatial manipulator are treated with this method.Key Words: Jacobian; Workspace; Singularities; Degree of freedomDOI: 10.3329/jme.v41i1.5359Journal of Mechanical Engineering, Vol. ME 41, No. 1, June 2010 25-30

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.

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

scholarly journals Modelling workflow forest fire soil - thrower with energy-saving hydraulic drive

2018 ◽  
Vol 7 (4) ◽  
pp. 182-189
Author(s):  
Петр Попиков ◽  
P. Popikov ◽  
П. Гончаров ◽  
P. Goncharov ◽  
Андрей Шаров ◽  
...  
Keyword(s):  
Energy Saving ◽  
Forest Fire ◽  
Hydraulic System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Hydraulic Drive ◽  
Spherical Shape ◽  
Algebraic Equations ◽  
Working Bodies ◽  
Three Dimensional Space

The article is a schematic diagram of the hydraulic soil-thrower with connection air-charged accumulator which stores energy during overload when working bodies meeting with obstacles, while avoiding the operation of safety valves and conversion hydraulic energy into heat. Mathematical model that comprehensively describes the events taking place: the rotation and movement of the rotor soil-thrower rotor interaction with the ground and obstacles, the drive ground in space. In the method of the soil and the obstacles presented a collection of a large number (about 2000 ... 10000) spherical elements of small size, enabled communicate both among themselves and with the blades soil-thrower. The simulation is performed in three-dimensional space XYZ, where in the same elements have a spherical shape with the same diameter. With in the framework of the model developed by the working surfaces are represented as a set of elementary triangles. Rotor soil-thrower model with some degree of desensitization is represented by four rectangular blades, each of which consists of two triangles. In the process of simulation reproduced rotation of the rotor and the calculation of the interaction with the elements of triangular surfaces ground and obstacles. To solve the system of differential-social and algebraic equations, which laid the basis for the model, time-operated computer program "Program for modeling the work of forest fire soil-thrower with energy saving action hydraulic drive" program time to work in Borland Delphi environment 7.0 language Object Programming PascalIzucheny soil-thrower stage of interaction with the irresistible preption. Using the powering hydraulic system improves the uniformity of rotation of the rotor, to reduce energy costs for rotorus rotation by 12%.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

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