Closure to “Discussion of ‘On a General Method of Spatial Kinematic Synthesis by Means of a Stretch-Rotation Tensor’” (1969, ASME J. Eng. Ind., 91, pp. 121–122)

1969 ◽  
Vol 91 (1) ◽  
pp. 122-122
Author(s):  
G. N. Sandor ◽  
K. E. Bisshopp
Keyword(s):  
Rotation Tensor ◽  
Kinematic Synthesis ◽  
General Method

On a General Method of Spatial Kinematic Synthesis by Means of a Stretch-Rotation Tensor

1969 ◽  
Vol 91 (1) ◽  
pp. 115-121 ◽  
Author(s):  
G. N. Sandor ◽  
K. E. Bisshopp
Keyword(s):  
Mathematical Model ◽  
Kinematic Chain ◽  
Higher Order ◽  
Motion Generation ◽  
Rotation Tensor ◽  
Kinematic Synthesis ◽  
Rotation Operator ◽  
Key Concepts ◽  
The Mathematical Model ◽  
General Method

One of the key concepts in a general method of spatial kinematic synthesis is a stretch-rotation operator applied to members of a general spatial kinematic chain. The latter consists of one or more interconnected loops of successively ball-jointed bar-slideball members. Each member is represented by a vector free to stretch-rotate with the motion of the chain. In the mathematical model of the general chain, displacement is simulated by means of stretch-rotation tensors operating on each member vector. Appropriate mathematical constraints render the general chain and its mathematical model equivalent to a particular mechanism. With this approach and by taking derivatives, first, second, and higher-order loop equations can be developed which form the basis for a general method of spatial kinematic synthesis, applicable to path, function and motion generation (body guidance) with first, second, and higher-order as well as for combined “point-order” approximations.

scholarly journals Method for the multi-criteria optimization of car wheel suspension mechanisms

2016 ◽  
Vol 36 (2) ◽  
pp. 60 ◽  
Author(s):  
Catalin Alexandru ◽  
Vlad Totu
Keyword(s):  
Computer Program ◽  
Kinematic Synthesis ◽  
Axis Direction ◽  
Car Body ◽  
Race Car ◽  
Design Variables ◽  
Kinematic Behavior ◽  
Kinematic Study ◽  
Kinematic Position ◽  
General Method

The paper deals with a general method for the multi-criteria optimization of the rear wheels suspension mechanisms in terms of kinematic behavior. The suspension mechanism is decomposed in basic binary links, and the kinematic synthesis is separately performed for each of them. The design variables are the global coordinates of the joint locations on the car body (chassis). The disposing of the joints on the wheel carrier were exclusively established by constructive criteria. The design objectives relate to kinematic position parameters of the wheel (displacements of the wheel centre along longitudinal and transversal directions, and modifications of the wheel axis direction), the optimization goal being to minimize these variations during the wheel travel. A computer program for the kinematic study was developed in C++. The application was performed for the wheel suspension mechanism of a race car.

General method for kinematic synthesis of manipulators with task specifications

Robotica ◽  
1997 ◽  
Vol 15 (6) ◽  
pp. 653-661 ◽  
Author(s):  
F.B. Ouezdou ◽  
S. Régnier
Keyword(s):  
Degrees Of Freedom ◽  
Inverse Kinematic ◽  
Synthesis Problem ◽  
Inverse Kinematic Problem ◽  
Kinematic Synthesis ◽  
Six Degrees Of Freedom ◽  
Cluttered Environment ◽  
Dimensional Parameters ◽  
Joint Limits ◽  
General Method

This paper deals with the kinematic synthesis of manipulators. A new method based on distributed solving is used to determine the dimensional parameters of a general manipulator which is able to reach a set of given tasks specified by orientation and position. First, a general Distributed Solving Method (DSM) is presented in three steps: the problem statement, the objective functions formulations and the minimum parameters values determination. Then, this method is applied to solve the synthesis of the Denavit and Hartenberg set of parameters of a manipulator with a given kinematic structure. In this case, the kind and the number of joints are specified and a set of constraints are included such as joint limits, range of dimensional parameters and geometrical obstacles avoidance. We show that if the Denavit and Hartenberg parameters (DH) are known, the synthesis problem is reduced to an inverse kinematic problem. We show also how the problem of robot base placement can be solved by the same method. A general algorithm is given for solving the synthesis problem for all kind of manipulators. The main contribution of this paper is a general method for kinematic synthesis of all kind of manipulators and some examples are presented for a six degrees of freedom manipulator in cluttered environment.

A New Method for Solving Mixed Sets of Equality and Inequality Constraints

1995 ◽  
Vol 117 (2A) ◽  
pp. 322-328 ◽  
Author(s):  
S. H. Mullins ◽  
W. W. Charlesworth ◽  
D. C. Anderson
Keyword(s):  
Inequality Constraints ◽  
Design Problems ◽  
Kinematic Synthesis ◽  
Modified Newton’S Method ◽  
Engineering Design Problems ◽  
Slack Variable ◽  
Equality And Inequality Constraints ◽  
Value Decomposition ◽  
Pseudo Inverse ◽  
General Method

Presented is a general method for solving sets of nonlinear constraints that include inequalities. Inequality constraints are common in engineering design problems, such as kinematic synthesis. The proposed method uses a modified Newton’s method and introduces a slack variable and a slack constraint to convert each inequality into an equality constraint. Singular value decomposition is used to find the pseudo-inverse of the Jacobian at each iteration. Benefits of this method are that constraint scaling is not an issue and that the method often fails gracefully for inconsistent constraint sets by providing direction for modification of the constraints so that an answer can be found. The method is also competitive with others in terms of the number of function evaluations needed to solve a set of problems taken from the literature.

High-Speed Mechanism Design—A General Analytical Approach

1975 ◽  
Vol 97 (2) ◽  
pp. 609-628 ◽  
Author(s):  
Imdad Imam ◽  
George N. Sandor
Keyword(s):  
High Speed ◽  
Optimization Problem ◽  
Design Procedure ◽  
Dynamic Stresses ◽  
Kinematic Synthesis ◽  
Elastic Links ◽  
High Speeds ◽  
Elastic Mechanism ◽  
Programming Techniques ◽  
General Method

A general method of kineto-elastodynamic design is developed and illustrated with examples. With this method, mechanisms with elastic links can be designed in a systematic way for a desired performance at high speeds. This is achieved by first performing the kinematic synthesis of the mechanism considering its links to be rigid, and then proportioning the areas of cross section of the links optimally to account for kineto-elastodynamic effects. Design optimization with respect to stress level, mass distribution and elastic deflections is performed by imposing constraints on dynamic stresses in every link and on the deflections of the path or function generating links throughout the range of motion. The optimization problem is formulated in terms of nonlinear programming techniques. Numerical examples are presented. The KED design procedure, which is developed and demonstrated here by way of several examples, is believed to be the first method of this kind for a completely elastic mechanism.

A simple and general method for kinematic synthesis of spatial mechanisms

1997 ◽  
Vol 32 (3) ◽  
pp. 323-341 ◽  
Author(s):  
J.M Jiménez ◽  
G Álvarez ◽  
J Cardenal ◽  
J Cuadrado
Keyword(s):  
Kinematic Synthesis ◽  
Spatial Mechanisms ◽  
General Method

A Unified Theory for the Finitely and Infinitesimally Separated Position Problems of Kinematic Synthesis

1969 ◽  
Vol 91 (1) ◽  
pp. 203-208 ◽  
Author(s):  
P. Chen ◽  
B. Roth
Keyword(s):  
Rigid Body ◽  
Companion Paper ◽  
Unified Theory ◽  
Kinematic Synthesis ◽  
Special Points ◽  
General Method

A rigid body is studied in a series of different positions. These positions can be finitely separated, infinitesimally separated, or a combination of the two. A general method for determining the locations of points or lines (in the rigid body) which have their different multiple positions satisfying the constraints of binary links or combined link chains is developed. In a companion paper [10] equations governing the locations of these special points and lines are derived.

A General Method for Spectrometer Design in the Scoff Approximation

1976 ◽  
Vol 34 ◽  
pp. 538-539
Author(s):  
J. R. Fields
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Energy Analysis ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Chemical Identification ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
General Method

The energy analysis of electrons scattered by a specimen in a scanning transmission electron microscope can improve contrast as well as aid in chemical identification. In so far as energy analysis is useful, one would like to be able to design a spectrometer which is tailored to his particular needs. In our own case, we require a spectrometer which will accept a parallel incident beam and which will focus the electrons in both the median and perpendicular planes. In addition, since we intend to follow the spectrometer by a detector array rather than a single energy selecting slit, we need as great a dispersion as possible. Therefore, we would like to follow our spectrometer by a magnifying lens. Consequently, the line along which electrons of varying energy are dispersed must be normal to the direction of the central ray at the spectrometer exit.

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