Singular Conditions and Solutions of the Standard Triad Displacement Equation

1990 ◽  
Vol 112 (4) ◽  
pp. 457-465 ◽  
Author(s):  
Chuen-Sen Lin ◽  
A. G. Erdman
Keyword(s):  
Angular Displacement ◽  
Dimensional Synthesis ◽  
Practical Solution ◽  
Numerical Example ◽  
Special Cases ◽  
Displacement Equation ◽  
Solution Methods ◽  
Angular Displacements

In the dimensional synthesis of a standard planar triad, if the prescribed angular displacements of two of the three links are the same at all precision positions or the prescribed angular displacements of one link are zero at all precision positions, the standard triad displacement equation will not yield a practical solution: a triad having all links with finite lengths. The displacement equation may also fail to generate a practical solution triad in case that the freely chosen angular displacement of one link equals to zero, or equals to the prescribed angular displacement of another link at the same precision position. In this paper, the special cases in the dimensional synthesis of a standard triad are discussed in detail, the types of triads which can generate the motions corresponding to the special cases are listed, and the solution methods to solve the displacement equations of the special types of triads are developed. Finally a numerical example is given to show the application of one of the special types of triad in the dimensional synthesis of an eight-bar linkage.

Control of processing at multi-tool two-support setup

2020 ◽  
pp. 67-73
Author(s):  
N.D. YUsubov ◽  
G.M. Abbasova
Keyword(s):  
Degrees Of Freedom ◽  
Factor Model ◽  
Angular Displacement ◽  
Factor Models ◽  
Technological System ◽  
Displacement Control ◽  
Model Accuracy ◽  
Six Degrees Of Freedom ◽  
Angular Displacements ◽  
And Control

The accuracy of two-tool machining on automatic lathes is analyzed. Full-factor models of distortions and scattering fields of the performed dimensions, taking into account the flexibility of the technological system on six degrees of freedom, i. e. angular displacements in the technological system, were used in the research. Possibilities of design and control of two-tool adjustment are considered. Keywords turning processing, cutting mode, two-tool setup, full-factor model, accuracy, angular displacement, control, calculation [email protected]

scholarly journals L’innovation et le modèle du commerce néo-technologique dans l’espace des caractéristiques de Lancaster

2009 ◽  
Vol 55 (3) ◽  
pp. 342-359
Author(s):  
Petr Hanel
Keyword(s):  
Necessary Conditions ◽  
New Product ◽  
Efficient Production ◽  
Numerical Example ◽  
Special Cases ◽  
Welfare Implications ◽  
Efficient Consumption

Lancaster's case of innovation in consumption technology is formalized and extended to include beside of the criterion of efficient consumption also the criterion of efficient production. The two criteria has to be met before an invention can be commercialized economically. Trade provoked by an innovation in consumption technology—a new product—is analyzed on a simple numerical example. Necessary conditions and some welfare implications of the neo-technology trade are presented. The approach is sufficiently general to encompass trade based on cost reducing innovation as well as existing trade models as special cases.

Synthesis of Parallel Manipulator with Single DOF

2013 ◽  
Vol 330 ◽  
pp. 639-643 ◽  
Author(s):  
Chung Huang Yu ◽  
Wen Yeuan Chung
Keyword(s):  
Parallel Manipulator ◽  
Design Concept ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Numerical Example ◽  
Geometrical Constraints ◽  
Moving Platform ◽  
Manipulator Design

This paper proposed a new manipulator design concept which leads to a single DOF system. The system composed of a moving platform and several supporting legs. It can execute the tasks of 3D body guidance or path generation and thus replace expensive manipulators with high DOF in some conditions. There are mainly two steps in designing this manipulator. The first step is type synthesis to determine the number and types of legs. Dimensional synthesis is then executed based on the movement requirements and geometrical constraints. In this study the reduction of the DOF is also analyzed for various legs added between the moving platform and the ground. A numerical example of executing 3D body guidance is given to verify the proposed new concept.

Analysis of Five-Degree-of-Freedom Robot Arms

1983 ◽  
Vol 105 (1) ◽  
pp. 23-27 ◽  
Author(s):  
K. Sugimoto ◽  
J. Duffy
Keyword(s):  
Arc Welding ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Industrial Robot ◽  
Degree Of Freedom ◽  
Numerical Example ◽  
Robot Arms ◽  
Special Cases ◽  
Computer Controlled ◽  
Five Axes

Many kinds of robot arms with five degrees of freedom are widely used in industry for arc welding, spray painting, assembling etc. It is necessary to be able to compute joint displacements when such devices are computer controlled. A solution to this problem is presented and the analysis is illustrated by a numerical example using the most common industrial robot with five axes. Further, special cases are discussed using screw theory.

A Proposed Method to Group the Solutions From Dimensional Synthesis: Planar Triads for Six Precision Position

1992 ◽  
Author(s):  
Xiancheng Lu ◽  
Chuen-Sen Lin
Keyword(s):  
Infinite Number ◽  
Numerical Solutions ◽  
Angular Displacement ◽  
Dimensional Synthesis ◽  
Number Of Solutions ◽  
Jacobian Matrices ◽  
Design Task ◽  
Numerical Examples ◽  
Computer Automation ◽  
Constraint Sets

Abstract In this paper, a method has been proposed to group into six sets the infinite number of solutions from dimensional synthesis of planar triads for six precision positions. The proposed method reveals the relationships between the different configurations of the compatibility linkage and the sets of numerical solutions from dimensional synthesis. By checking the determinant signs and the contunities of values of the sub-Jacobian matrices and their derivatives with respect to the independent angular displacement for all constraint sets in the compatibility linkage, it enables the computer to identify and group the synthesized solutions. Numerical examples have been given to verify the applicability of this method. Six sets of the partial triad Burmester curves have been plotted based on grouped solutions. Suitable solutions can be easily found from the partial triad Burmester curves and utilized for the prescribed design task. This method provides a useful tool to group the dimensional synthesis solutions and enhances the computer automation in the design of linkage mechanisms.

Displacement Analysis of Two Special Cases of the TTTR Mechanisms

1989 ◽  
Vol 111 (3) ◽  
pp. 309-314 ◽  
Author(s):  
Wei Lin ◽  
Joseph Duffy
Keyword(s):  
Angular Displacement ◽  
Displacement Analysis ◽  
Special Cases ◽  
Quartic Polynomials

A pair of quartic polynomials in the tangent of the output angular displacement were derived for two TTTR mechanisms designed in such a way that the serially connected pairs of Hooke joints have their successive transverse axes parallel or mutually perpendicular. These results form the basis for an efficient reverse displacement analysis and for the design of a new group of robots with three serially connected Hooke joints which may prove to be attractive to industry.

scholarly journals BIOMECHANICAL EFFECTS OF HYPERPRONATION ON MULTIDIRECTIONAL ANKLE ANGULAR DISPLACEMENT AND STIFFNESS

2020 ◽  
Vol 20 (09) ◽  
pp. 2040012
Author(s):  
GEON KIM ◽  
JIHEE JUNG ◽  
YOUNGJOO CHA ◽  
JOSHUA (SUNG) H. YOU
Keyword(s):  
Sagittal Plane ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Frontal Plane ◽  
Neutral Group ◽  
Stiffness Reduction ◽  
Ankle Stiffness ◽  
Foot Injury ◽  
Increased Risk ◽  
Angular Displacements

Hyperpronation of the foot is believed to contribute to ankle hypermobility and associated stiffness reduction, but the underlying biomechanical mechanisms remain unknown. This study aimsed to investigate multidirectional ankle displacement and associated stiffness when a posterior–anterior impact force was applied to the posterior knee compartment. Forty healthy adults with and without foot hyperpronation were recruited. A three-dimensional motion capture system and force plates were used to acquire angular displacement and ankle joint moment data. The independent [Formula: see text]-test and Mann–Whitney [Formula: see text] test were used to compare the group differences in ankle angular displacement, moment, and stiffness. Spearman’s rho test was performed to determine the relationship between ankle angular displacement and stiffness. The hyperpronation group demonstrated significantly greater sagittal ([Formula: see text]) and frontal plane ([Formula: see text]) angular displacements and reduced sagittal plane ankle stiffness ([Formula: see text]) than the neutral group. The Spearman’s correlation analysis showed a close inverse relationship between the ankle angular displacement and stiffness, ranging from [Formula: see text] to [Formula: see text]. The biomechanical data in our study suggest that individuals with foot hyperpronation present with multidirectional hypermobility and a reduction in ankle stiffness. These factors contribute to an increased risk of ankle-foot injury in individuals with foot hyperpronation.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

Flow in a Toroidal Thermosyphon with Angular Displacement of Heated and Cooled Sections

1979 ◽  
Vol 101 (4) ◽  
pp. 672-676 ◽  
Author(s):  
P. S. Damerell ◽  
R. J. Schoenhals
Keyword(s):  
Steady State ◽  
Reverse Flow ◽  
Angular Displacement ◽  
Vertical Plane ◽  
Steady Condition ◽  
Steady State Flow ◽  
Flow Rates ◽  
Flow Phenomenon ◽  
Angular Displacements ◽  
Good Agreement

A toroidal thermosyphon consisting of a fluid-filled torus located in a vertical plane was studied analytically and experimentally. Good agreement was obtained between analytical predictions and measurements for large values of the angular displacement of the heated and cooled sections. For smaller angular displacements, the analytical predictions of steady state flow rates were found to exceed the corresponding experimentally observed values. The discrepancies were attributed to a reverse flow phenomenon. Some analytically predicted flows were not physically achievable. In these situations the flow would either reach a steady condition in the opposite direction, or it would oscillate indefinitely.

The RCRRC Five-Link Space Mechanism—Displacement Analysis, Force and Torque Analysis and Its Transmission Criteria

1975 ◽  
Vol 97 (2) ◽  
pp. 581-594 ◽  
Author(s):  
Ing-Ping Jack Lee ◽  
Cemil Bagci
Keyword(s):  
Angular Displacement ◽  
Unified Theory ◽  
Eighth Order ◽  
Joint Force ◽  
Output Displacement ◽  
Displacement Equation ◽  
The Matrix ◽  
Torque Analysis ◽  
Force Components ◽  
Inertia Forces

Displacement, and force and torque analyses of the RCRRC five-link space mechanism are performed using 3 × 3 screw matrix and dual vectors. Expressions for all the displacements in the mechanism are given. Input-output displacement equation is obtained in both eighth order and 16th order polynomials in half-tangents of the angular displacement. The solution of the 16th order displacement equation shows that the RCRRC mechanism may have 16 geometric inversions for a set of dimensions. The eighth order displacement equation, which conforms with that obtained by the Unified Theory which uses dual spherical trigonometry, is an incomplete relationship and it only gives the displacements of half of the existing geometric inversions. Numerical examples and photographs of the geometric inversions are given. The force and torque analysis of the RCRRC five-link space mechanism is performed by joint force analysis. Dual inertia forces are neglected, and the motion of the mechanism is known. Explicit expressions for the dual force components at the pair locations are given, as well as the matrix solution. Transmissivities of the mechanism are defined. Force and torque analysis of one of the geometric inversions is performed in a numerical example.

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