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.

A Displacement Analysis of Spatial Six-Link 4-R-P-C Mechanisms—Part 2: Derivation of Input-Output Displacement Equation for RCRRPR Mechanism

1974 ◽  
Vol 96 (3) ◽  
pp. 713-717 ◽  
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Angular Displacement ◽  
Input Output ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Displacement Equation

The input-output displacement equation is expressed as a degree eight polynomial in the half-tangent of the output angular displacement. The equation can be used to generate input-output functions of spatial five-link RCRCR and RCRRC mechanisms. The results are illustrated by numerical examples.

A Displacement Analysis of Spatial Six-Link 4R-P-C Mechanisms—Part 1: Analysis of RCRPRR Mechanism

1974 ◽  
Vol 96 (3) ◽  
pp. 705-712 ◽  
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Angular Displacement ◽  
Physical Significance ◽  
Input Output ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spherical Mechanisms ◽  
Displacement Equation

The input-output displacement equation is expressed as a degree eight polynomial in the half-tangent of the output angular displacement. A procedure for determining uniquely all the linkage variables verifies the closures and in addition explains the physical significance of the closures of equivalent five-link R5 spherical mechanisms. The equation can be used to generate input-output functions of spatial five-link RCCRR and RCRCR mechanisms. The results are illustrated by numerical examples.

A Displacement Analysis of Spatial Six-Link 4R-P-C Mechanisms—Part 3: Derivation of Input-Output Displacement Equation for RRRPCR Mechanism

1974 ◽  
Vol 96 (3) ◽  
pp. 718-721 ◽  
Author(s):  
J. Duffy ◽  
J. Rooney
Keyword(s):  
Angular Displacement ◽  
Output Function ◽  
Input Output ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Displacement Equation

The input-output displacement equation is expressed as a degree eight polynomial in the half-tangent of the output angular displacement. The equation can be used to generate the input-output function for the spatial five-link RRCCR mechanism. The results are illustrated by numerical examples.

Displacement Analysis of the RRCCR Five-Link Spatial Mechanism

1970 ◽  
Vol 37 (3) ◽  
pp. 689-696 ◽  
Author(s):  
M. S. C. Yuan
Keyword(s):  
Input Output ◽  
Eighth Order ◽  
Variable Parameters ◽  
Displacement Analysis ◽  
Output Displacement ◽  
Spatial Mechanism ◽  
Input And Output ◽  
Displacement Equation ◽  
Order Polynomial

By the method of line coordinates, the input-output displacement equation of the RRCCR five-link spatial mechanism is obtained as an eighth-order polynomial in the half tangent of the output angle. For each set of the input and output angles obtained from the polynomial, all other variable parameters of the mechanism are uniquely determined, and the accuracy of the numerical values of each set of solutions is verified.

Diamond tool wear monitoring by sensory analysis in milling of absolute black granite

2021 ◽  
pp. 095440542110406
Author(s):  
Sandro Turchetta ◽  
Luca Sorrentino ◽  
Gianluca Parodo
Keyword(s):  
Tool Wear ◽  
Cutting Tools ◽  
Depth Of Cut ◽  
Surface Machining ◽  
Diamond Tools ◽  
The Matrix ◽  
Cutting Force Components ◽  
Force Components ◽  
Natural Stones ◽  
And Performance

Diamond tools suitable for machining operations of natural stones can be divided into two groups: cutting tools, including blades, the circular blades and the wires, and the surface machining ones, involving mills and grinders, that can be of different shapes. For the stone sawing process, the most adopted tool type is the diamond mill, whose duration and performance are influenced by various elements such as: the mineralogical characteristics of the material to be machined; the working conditions such as the depth of cut, the feed rate and the spindle speed; the production process of the diamond segment and the characteristics of both the matrix and the diamond, such as the size, the type and the concentration of the diamonds and the metal bond formulation hardness. This work allows to indirectly assess the wear of sintered diamond tools by signal analysis (in time and frequency domain) of the cutting force components acquired in the process. The results obtained represent a fundamental step for the development of a sensory supervision system capable of assessing the tool wear and hence to modify the process parameters in process, in order to optimize cutting performance and tool life.

Simulation and Experimental Study of the Coupling Drive Magnetic Field for Embedded Giant Magnetostrictive Actuators

2012 ◽  
Vol 510 ◽  
pp. 322-327
Author(s):  
Bin Wang ◽  
Yi Jie Wu ◽  
Lei Zhang
Keyword(s):  
Magnetic Field ◽  
Matrix Material ◽  
Experimental Tests ◽  
High Frequencies ◽  
Output Displacement ◽  
Close Relationship ◽  
The Matrix ◽  
Magnetostrictive Actuators ◽  
Magnetostrictive Actuator ◽  
The Relationship

Embedded giant magnetostrictive actuator (EGMA) is one of the most important applications of magnetostrictive material. Giant magnetostrictive actuators can deliver big-output displacement and can be driven at high frequencies. These characteristics make them suitable for a variety of positioning. However, because of the limitation of structure, the drive coil and EGMA cannot be any size as needed, so how to maximize the displacement in the limitative situation by optimization becomes the key of design. Several methods are available in the literature, but the coupling drive magnetic field of EGMA and its matrix material is often ignored. In fact, there was a close relationship between the matrix material and the distribution of drive magnetic field. To analyze the relationship, this paper establishes the magnetic circuit model for EGMA. The simulation of the coupling drive magnetic field is also presented. Finally the assumption is validated through experimental tests carried out with two different matrix materials.

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.

Internal Force and Moment Transmission in a Cardan Joint With Manufacturing Tolerances

1984 ◽  
Vol 106 (3) ◽  
pp. 301-311 ◽  
Author(s):  
I. S. Fischer ◽  
F. Freudenstein
Keyword(s):  
Internal Force ◽  
Design Stage ◽  
Force Transmission ◽  
Displacement Analysis ◽  
Joint Forces ◽  
Torque Transmission ◽  
Torque Analysis ◽  
Manufacturing Tolerances ◽  
Force Components ◽  
Cardan Joint

The literature on the internal forces in Cardan joints, which is sparse, tacitly assumes the vanishing of certain force components. For a joint of ideal proportions the torque transmission has been analyzed, but the force transmission has been only partially developed. In this investigation the displacement analysis and static force and torque analysis of a Cardan joint with manufacturing tolerances has been derived. The forces have been shown to be statically indeterminate by a degree of three. An experiment was undertaken to check on the validity of the assumed vanishing of the abovementioned force components. For the particular joint tests this assumption was not valid. Based on the displacement analysis, which includes the axial sliding at the joints in the presence of manufacturing errors, optimum tolerances can be determined in the design stage. Further experimentation is recommended in order to determine representative magnitudes of the abovementioned axial joint forces in joints of varying constructions and sizes. Together with the static analysis which has been developed in this investigation this will permit the sizing of universal joints in the design stage.

Gross-Motion Dynamic Response Analysis of Indeterminate Mechanisms by Matrix Displacement Method

1975 ◽  
Vol 97 (2) ◽  
pp. 682-688
Author(s):  
R. L. Brasfield ◽  
Cemil Bagci
Keyword(s):  
Dynamic Response ◽  
Response Analysis ◽  
Force Analysis ◽  
Initial Value ◽  
Small Oscillations ◽  
Dynamic Response Analysis ◽  
Joint Force ◽  
Solution Of Equations ◽  
The Matrix ◽  
Space Mechanisms

A method of gross-motion dynamic response analysis of indeterminate space mechanisms, as well as indeterminate plane mechanisms with offsets of links, to specified input forces or torques, such as in mechanisms of automated systems, mechanical robots, and switching mechanisms, is presented. The method uses joint force analysis along with the matrix displacement-direct element method. Unknown motion of the mechanism as function of time is determined by the solution of equations of gross-motion as an initial value problem. The effect of small oscillations of a link about an equilibrium position is neglected. An indeterminate plane four-bar and the indeterminate Bennett mechanisms are analyzed as switching mechanisms in the numerical examples.

Multiparameter Sturm theory

1984 ◽  
Vol 99 (1-2) ◽  
pp. 173-184 ◽  
Author(s):  
Paul Binding ◽  
Patrick J. Browne
Keyword(s):  
Elliptic Partial Differential Equation ◽  
Comparison Theorems ◽  
Unified Theory ◽  
Focal Points ◽  
The Matrix ◽  
Sturm Liouville ◽  
Left And Right ◽  
Image Position ◽  
Completeness Of Eigenfunctions ◽  
Sturm Theory

SynopsisLet Sturm–Liouville problemswith continuous coefficients and appropriate boundary conditions, be coupled by the eigenvalue λ = (λ1, … λk). When k = 1, there are various oscillation, perturbation and comparison theorems concerning existence and continuous or monotonic dependence of eigenvalues, eigenfunctions and their zeros (i.e. focal points).We attempt a unified theory for such results, valid for general fc, under conditions known as "left" and “right” definiteness. A representative result may be stated loosely as follows: if LD holds then (elementwise) monotonic dependence of p, q and the matrix [ars] forces monotonic dependence of λ. LD is a generalisation of the “polar” case for k = 1, and was originally conceived for a quite different purpose, viz. completeness of eigenfunctions via elliptic partial differential equation theory.

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