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.

Principles of a General Quaternion-Operator Method of Spatial Kinematic Synthesis

1968 ◽  
Vol 35 (1) ◽  
pp. 40-46 ◽  
Author(s):  
George N. Sandor
Keyword(s):  
Operator Method ◽  
Kinematic Chain ◽  
Point Theory ◽  
System Of Equations ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Special Cases ◽  
General Complex ◽  
Spatial Method ◽  
Space Mechanisms

The basic concepts of a general method of kinematic synthesis of space mechanisms are developed by means of vectors and quaternion operators applicable to path, function, and motion generation (body guidance) for finite and infinitesimal displacements (point, order, and combined point-order approximations). For writing the position equations, space mechanisms are represented by one or more loops of a general kinematic chain of ball-jointed bar-slideball members. Appropriate mathematical constraints on the relative freedom of these members render the general chain equivalent to the represented mechanism. The method leads to a system of equations of canonical simplicity, uniform for all tasks of finite spatial synthesis, often yielding closed-form linear solutions for small numbers of precision conditions. The same system of equations is then used to refine the solution for greater precision by numerical methods. Typical applications are indicated, some involving the use of a spatial finite circlepoint-center point theory, which includes classical planar Burmester theory as one of its special cases. An earlier general complex-number method of planar synthesis is shown to be a special case of the general spatial method introduced here.

Beam Theories for Torsional-Bending Response of Ship Hulls

1991 ◽  
Vol 35 (03) ◽  
pp. 254-265 ◽  
Author(s):  
P. Terndrup Pedersen
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Response Analysis ◽  
Element Formulation ◽  
Transition Matrices ◽  
Ship Hulls ◽  
The Mathematical Model ◽  
Bending Response

A consistent one-dimensional finite-element procedure for analysis of the coupled torsional-bending response of thin-walled beam structures such as ship hulls is presented. At each element end there are three translations, three rotations and one classical Vlasov warping degree of freedom plus possibly N degrees of freedom associated with higher order generalized warping deformation modes. These higher order warping modes are generated from an eigenvalue problem associated with the homogeneous plane stress equilibrium condition for the individual beam cross sections. The assembly of the beam elements to the global model is performed by use of transition matrices which assure compatibility between the elements in the sense of least squares. Numerical examples are included which demonstrate the accuracy of the mathematical model and the applicability of the proposed analysis procedure for calculation of torsion-horizontal bending response of a containership hull. Even if the higher order warping modes are not included in the finite element formulation it is found that the mathematical model is quite accurate for overall response analysis of hull structures.

Mathematical Model for Parametric Tooth Surface of Cylindrical Gears Based on Kinematic Synthesis

2007 ◽  
Author(s):  
Carlos Garci´a-Masia´ ◽  
Juan D. Morillas-A´lvarez
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Asymmetry Ratio ◽  
Contact Ratio ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Transmission Errors ◽  
Cylindrical Gears ◽  
Tooth Surfaces ◽  
And Function

A generalized approach for parametrizing conjugate tooth surfaces in cylindrical gears is presented in this work. Developed are the polynomials expressions to define the tooth surfaces of pinion and gear based on kinematics synthesis for planar gears. The polynomials expressions incorporate the motion generation (points or positions of precision) and function of transmission errors. It is interesting to note that if the desired pressure angle for the tooth profile is constant, the output polynomial of profile becomes a conventional involute. Polynomials expressions are given for the profile modifications necessary to compensate for any specified or anticipated errors of assembly and/or manufacturing. In addition property of rack as the limits of zone active, transverse contact ratio and contact asymmetry ratio are analysed.

Robust Design of 4-Position Motion Generation and Application on Front End Loader

2012 ◽  
Vol 220-223 ◽  
pp. 736-739
Author(s):  
Wei Xiang Qian
Keyword(s):  
Mathematical Model ◽  
Optimum Design ◽  
Robust Design ◽  
Design Approach ◽  
Engineering Practice ◽  
Motion Generation ◽  
Robust Solution ◽  
Kinematic Accuracy ◽  
Front End ◽  
The Mathematical Model

A robust design approach of 4-position motion generation is presented, and it is applied in the design of front end loader. The mathematical model of optimum design based upon the engineering requirements has been established, by which feasible robust solution regions adhering to conventional constraints and kinematic accuracy requirements can be visually represented. It guides designers to synthesize robust mechanisms that ensure every design condition. The example of front end loader demonstrates that the process of searching the optimal robust mechanism is more intuitive, highly accessible and easy to be applied in engineering practice.

scholarly journals Mathematic model of three-phase induction machine connected to advanced inverter for traction system for electric trolley

2013 ◽  
Vol 85 (2) ◽  
pp. 849-858 ◽  
Author(s):  
LIVIU S. BOCII ◽  
VALENTIN MULLER
Keyword(s):  
Mathematical Model ◽  
Electric Motor ◽  
Induction Machine ◽  
Mathematic Model ◽  
Higher Order ◽  
Motor Drive ◽  
Operating Characteristics ◽  
Electric Motor Drive ◽  
The Mathematical Model ◽  
Frequency Inverter

This paper establishes a mathematical model of induction machine connected to a frequency inverter necessary to adjust the electric motor drive. The mathematical model based on the Park's theory allows the analysis of the whole spectrum (electric car – frequency inverter) to drive the electric trolley bus made on ASTRA Bus Arad (Romania). To remove higher order harmonics, the PWM waveform of supply voltage is used, set in the general case. Operating characteristics of electric motor drive are set to sub-nominal frequency (f < 50 Hz) and for different angles of the control switching elements in the construction of the inverter. Tensions in the stator of the equivalent machine are determined by three components: the fundamental component; the second component corresponding to the higher order harmonics, which rotate in direct connection; and the appropriate third component of higher order harmonics, which are rotated in reverse. The mathematical model developed will help to determine the harmonics which have a negative influence on the performance of the electric engine and also determines the control angle of the switching elements to remove these harmonics, (Bele 2007).

A General Method for Optimum Design of Gear Boxes Through Nonlinear Programming

1989 ◽  
Author(s):  
W. L. Cleghorn ◽  
R. G. Fenton ◽  
J.-F. Fu
Keyword(s):  
Mathematical Model ◽  
Nonlinear Programming ◽  
Optimum Design ◽  
Random Search ◽  
Optimization Methods ◽  
Search Method ◽  
Programming Technique ◽  
Tolerance Method ◽  
The Mathematical Model ◽  
General Method

Abstract A general method for the optimum design of gear boxes is presented using a nonlinear programming technique. The mathematical model of the gear box is developed using a symbolic mathematical manipulator. Constraints of the feasible design have been included but reduced to be as few as possible. Identical optimum results were obtained through employing two different optimization methods, the flexible tolerance method and the random search method, for solving an example problem.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

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