Static Force and Torque Analysis Using 3 × 3 Screw Matrix, and Transmission Criteria for Space Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 90-101 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Static Force ◽  
Equilibrium Equations ◽  
Torque Distribution ◽  
Dual Vector ◽  
Output Torque ◽  
Transmission Angle ◽  
Torque Analysis ◽  
Force Components ◽  
Space Mechanisms ◽  
Input Torque

The method of determining the static force and torque distributions in space mechanisms by use of the 3 × 3 screw matrix is presented. Transmissivities in favor of rotation and translation, and angles of transmission in space mechanisms are defined. Transmissivities are used to show why some space mechanisms have no dead center positions. In the process, the dual equilibrium equations, one for each link, are written in dual vector form, then they are solved simultaneously for the dual force components. Explicit expressions for forces and torques in the RCCC and RSSR space mechanisms are obtained. Torque distribution in the spherical four-bar mechanism is reduced from the results for the RCCC space mechanism. The numerical example considers a symmetrical crank-rocker RSSR space mechanism, where the output torque is due to the load inertia. Variations in the input torque, output torque, mechanical advantage, and transmission angle for one cycle are given for both geometric inversions.

Dynamic Force and Torque Analysis of Mechanisms Using Dual Vectors and 3 × 3 Screw Matrix

1972 ◽  
Vol 94 (2) ◽  
pp. 738-745 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Rate Of Change ◽  
Inertia Force ◽  
Dynamic Force ◽  
Equilibrium Equations ◽  
Force Vector ◽  
Time Rate ◽  
Output Force ◽  
Dynamic Analyses ◽  
Torque Analysis ◽  
Space Mechanisms

The method of determining dynamic force and torque distributions in mechanisms by using dual vectors and 3 × 3 screw matrix is presented. The dual equilibrium equations for each moving link of a mechanism are written as a null resultant dual force vector in a reference system located on the link. The resulting 6 × (n – 1) equilibrium equations for an n-link mechanism are solved for the unknown force and torque components at the pair locations, and for the input force or torque required to drive the mechanism to produce the specified dual output force. The dynamics of the mechanism is governed by introducing the dual inertia force acting on a link, which is determined as the negative of the time rate of change in the dual momentum of the link due to its own mass and mass moments of inertia, in the dual equilibrium equation for that link. Dynamic analyses of the 4R plane and the RCCC space mechanisms are performed. Dynamic transmissivities are defined. The RCCC mechanism is analyzed in a numerical example and the results of the dynamic distributions are compared with those of static distributions.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

scholarly journals Analysis of the Single Toggle Jaw Crusher Force Transmission Characteristics

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Moses Frank Oduori ◽  
David Masinde Munyasi ◽  
Stephen Mwenje Mutuli
Keyword(s):  
Mean Value ◽  
Force Transmission ◽  
Transmission Characteristics ◽  
Dead Weight ◽  
Mechanical Advantage ◽  
Jaw Crusher ◽  
Output Torque ◽  
The Mean ◽  
Balance Of Forces ◽  
Input Torque

This paper sets out to perform a static force analysis of the single toggle jaw crusher mechanism and to obtain the force transmission characteristics of the mechanism. In order to obtain force transmission metrics that are characteristic of the structure of the mechanism, such influences as friction, dead weight, and inertia are considered to be extraneous and neglected. Equations are obtained by considering the balance of forces at the moving joints and appropriately relating these to the input torque and the output torque. A mechanical advantage, the corresponding transmitted torque, and the variations thereof, during the cycle of motion of the mechanism, are obtained. The mechanical advantage that characterizes the mechanism is calculated as the mean value over the active crushing stroke of the mechanism. The force transmission characteristics can be used as criteria for the comparison of different jaw crusher mechanism designs in order to select the most suitable design for a given application. The equations obtained can also be used in estimating the forces sustained by the components of the mechanism.

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.

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.

Analysis and Visualization of the Contact Force Solution Space for Multi-Limbed Mobile Robots With Three Feet Contact

2003 ◽  
Author(s):  
Dennis W. Hong ◽  
Raymond J. Cipra
Keyword(s):  
Contact Force ◽  
Dimensional Space ◽  
Contact Point ◽  
Solution Process ◽  
Solution Space ◽  
Contact Forces ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Force Components ◽  
The Relationship

A new analytical method for determining, describing, and visualizing the solution space for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The foot contact forces are first resolved into strategically defined foot contact force components to decouple them for simplifying the solution process, and then the static equilibrium equations are applied to find certain contact force components and the relationship between the others. Using the friction cone equation at each foot contact point and the known contact force components, the problem is transformed into a geometrical one to find the ranges of contact forces and the relationship between them that satisfy the friction constraint. Using geometric properties of the friction cones and by simple manipulation of their conic sections, the whole solution space which satisfies the static equilibrium and friction constraints at each contact point can be found. Two representation schemes, the “force space graph” and the “solution volume representation,” are developed for describing and visualizing the solution space which gives an intuitive visual map of how well the solution space is formed for the given conditions of the system.

Forces and Moments at the Knee and Boot Top: Models for an Alpine Skiing Population

1997 ◽  
Vol 13 (3) ◽  
pp. 373-384 ◽  
Author(s):  
Albert G. Yee ◽  
C. Daniel Mote
Keyword(s):  
Injury Prevention ◽  
Regression Models ◽  
Bending Moment ◽  
Alpine Skiing ◽  
Static Force ◽  
Static Moment ◽  
Load Component ◽  
The Subject ◽  
Measured Force ◽  
Force Components

The purpose of this study was to identify regression models to predict moments at the boot top and knee from the force components at the bindings for a sample of skiers. Six subjects skied a slalom course, first with their boots set to the least stiff setting and then with their boots set to the most stiff setting. Six load component dynamometers measured force and moment components at the toe and heel bindings. An electrogoniometer measured ankle flexion. Regression models were developed for the subject sample that predicted quasi-static moment components at the boot top and knee from measurements of ankle flexion and the quasi-static force components at the bindings. Large anterior bending moment was not necessarily accompanied by large ankle flexion, which emphasized that binding designs and standards for injury prevention must account for forces and moments at the sites of potential injury, rather than limiting consideration to boot stiffness or forces at the bindings.

Analysis of Force Components in Bar Turning

1973 ◽  
Vol 95 (4) ◽  
pp. 960-964
Author(s):  
A. B. Husein ◽  
M. F. DeVries ◽  
S. M. Wu
Keyword(s):  
Separation Method ◽  
Equilibrium Equations ◽  
Oblique Cutting ◽  
Contact Surfaces ◽  
Force Components ◽  
Bar Turning

This paper presents the development of equilibrium equations permitting the determination of the force components at each of the chip-tool-workpiece contact surfaces in bar turning. The analysis is an extension of the force separation method developed for the oblique cutting of tubes. The solution presented is applicable to both bar and tube cutting and was experimentally evaluated. The bar turning data produced solutions that compared favorably with tube turning data obtained.

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