Kinematic Synthesis of Spherical Two-Gear Drives With Prescribed Entire-Motion Characteristics: Unlimited Crank Rotations and Optimum Transmission. Part 1: Theory

1986 ◽  
Vol 108 (1) ◽  
pp. 46-52 ◽  
Author(s):  
T. W. Lee ◽  
E. Akbil
Keyword(s):  
Rational Design ◽  
Transmission Characteristics ◽  
Kinematic Synthesis ◽  
Input And Output ◽  
Special Cases ◽  
Transmission Part ◽  
Motion Characteristics ◽  
Gear Drives ◽  
Algebraic Solutions

This investigation is concerned with the determination of the rotatability of the input and output cranks and the optimization of transmission characteristics of spherical two-gear drives. Algebraic solutions are shown to be feasible only in a few special cases. In general, numerical synthesis procedures, involving either optimization or parameter scanning processes, are essential and they are developed from the general theory presented in this paper. The results, including conditions that can be regarded as an extension of the Grashof’s rule to the class of spherical geared mechanisms, are useful for the rational design of mechanisms. Applications of the theory to practical mechanisms design are given in Part 2.

Kinematic Synthesis of Spherical Two-Gear Drives With Prescribed Entire-Motion Characteristics: Unlimited Crank Rotations and Optimum Transmission. Part 2: Applications

1986 ◽  
Vol 108 (1) ◽  
pp. 53-59 ◽  
Author(s):  
T. W. Lee ◽  
E. Akbil
Keyword(s):  
Design Procedure ◽  
Companion Paper ◽  
Analytical Investigation ◽  
Design Guidelines ◽  
Kinematic Synthesis ◽  
Computer Aided Analysis ◽  
Transmission Part ◽  
Motion Characteristics ◽  
Gear Drives ◽  
Insight Into

The theory developed in Part 1 [1] as well as in a companion paper [2] has been applied to the kinematic synthesis of a special class of spherical two-gear drives, including the Rotary Step Mechanism, with prescribed entire-motion characteristics. Insight into the behavior of such mechanisms can be interpreted through the results of an analytical investigation of mechanism characteristics. A useful design procedure, a design table, and a set of design guidelines are presented. Examples are given to illustrate both the analytical synthesis and the computer-aided analysis procedures.

Kinematic Synthesis of Spherical Two-Gear Drives With Prescribed Entire-Motion Characteristics: Displacement Analysis and Dwell Characteristics

1983 ◽  
Vol 105 (4) ◽  
pp. 663-671 ◽  
Author(s):  
T. W. Lee ◽  
E. Akbil
Keyword(s):  
Kinematic Synthesis ◽  
Displacement Analysis ◽  
Gear Drive ◽  
Transmission Angle ◽  
Computer Aided ◽  
Displacement Equation ◽  
Synthesis Procedure ◽  
Motion Characteristics ◽  
Joint Consideration ◽  
Gear Drives

This paper presents an analytical and computer-aided procedure on the kinematic synthesis of the spherical two-gear drive with prescribed dwell characteristics. The first part gives a displacement analysis which includes an investigation of the general case of spherical five-link, 5R mechanisms and the spherical geared five-link case. Two approaches, one making use of the spherical trigonometric relations and the other involving sequential coordinate transformations by real and orthogonal [3 × 3] matrices, yield identical input-output expressions. The remainder of the paper focuses on the dwell characteristics of the spherical two-gear drive using algebraic methods based on the displacement equation. Dwell criteria for the general mth-order dwell are derived. A specific example which involves a joint consideration of other entire-motion characteristics, such as limit positions and transmission-angle variations, is given to illustrate both the theory as well as the computer-aided synthesis procedure.

Kinematic Synthesis of Planar Two-Gear Drives With Prescribed Dwell Characteristics

1982 ◽  
Vol 104 (4) ◽  
pp. 687-697
Author(s):  
T. W. Lee ◽  
Y. Shereshevsky
Keyword(s):  
Velocity Fluctuation ◽  
Kinematic Synthesis ◽  
Numerical Examples ◽  
Design Chart ◽  
Gear Drive ◽  
Computer Aided ◽  
Motion Characteristics ◽  
Gear Drives ◽  
Four Bar Linkage ◽  
Analysis Of Motion

This paper presents an analytical and computer-aided procedure on the kinematic synthesis of the planar two-gear drive. The drive is designed as a reversing mechanism and as a nonreversing mechanism either with or without dwell. Dwell characteristics of the mechanism are investigated using algebraic methods. It is found that the problem relates closely to the velocity-fluctuation of the four-bar linkage. Both general and specific dwell criteria are derived. An efficient computer-aided procedure can be used for the analysis of motion characteristics and for the development of a design chart. Numerical examples illustrate both analytical as well as graphical synthesis procedures.

Analytical Techniques for the Optimisation of Rocket Trajectories

1963 ◽  
Vol 14 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Derek F. Lawden
Keyword(s):  
Gravitational Field ◽  
Artificial Satellite ◽  
Analytical Techniques ◽  
Present Position ◽  
Mayer Problem ◽  
Special Cases ◽  
Minimum Expenditure ◽  
Law Of Attraction ◽  
Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

scholarly journals РОЗРОБКА І СИНТЕЗ НОВОГО МЕХАНІЗМУ ТРАНСПОРТУ ШВЕЙНОЇ МАШИНИ

2019 ◽  
Vol 126 (5) ◽  
pp. 33-39
Author(s):  
В. А. Горобець ◽  
В. М. Дворжак
Keyword(s):  
Kinematic Parameters ◽  
Kinematic Synthesis ◽  
Sewing Machine ◽  
Movement Mechanism

To develop a new structure of the movement mechanism of the sewing machine materials, which provides a qualitative movement and perform a determination of its kinematic parameters. The  object  of  the  study  is  a  typical  and  developed  by  the  authors  mechanism  for moving materials sewing machines. To determine the parameters of the new mechanism, known methods of optimization kinematic synthesis of lever mechanisms are used.

scholarly journals Algebraically Solvable Problems: Describing Polynomials as Equivalent to Explicit Solutions

10.37236/734 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Uwe Schauz
Keyword(s):  
Combinatorial Nullstellensatz ◽  
Algebraic Solution ◽  
Explicit Solutions ◽  
Polynomial Map ◽  
Combinatorial Number Theory ◽  
Special Cases ◽  
The Matrix ◽  
Grid Points ◽  
Algebraic Solutions ◽  
Solvable Problems

The main result of this paper is a coefficient formula that sharpens and generalizes Alon and Tarsi's Combinatorial Nullstellensatz. On its own, it is a result about polynomials, providing some information about the polynomial map $P|_{\mathfrak{X}_1\times\cdots\times\mathfrak{X}_n}$ when only incomplete information about the polynomial $P(X_1,\dots,X_n)$ is given.In a very general working frame, the grid points $x\in \mathfrak{X}_1\times\cdots\times\mathfrak{X}_n$ which do not vanish under an algebraic solution – a certain describing polynomial $P(X_1,\dots,X_n)$ – correspond to the explicit solutions of a problem. As a consequence of the coefficient formula, we prove that the existence of an algebraic solution is equivalent to the existence of a nontrivial solution to a problem. By a problem, we mean everything that "owns" both, a set ${\cal S}$, which may be called the set of solutions; and a subset ${\cal S}_{\rm triv}\subseteq{\cal S}$, the set of trivial solutions.We give several examples of how to find algebraic solutions, and how to apply our coefficient formula. These examples are mainly from graph theory and combinatorial number theory, but we also prove several versions of Chevalley and Warning's Theorem, including a generalization of Olson's Theorem, as examples and useful corollaries.We obtain a permanent formula by applying our coefficient formula to the matrix polynomial, which is a generalization of the graph polynomial. This formula is an integrative generalization and sharpening of:1. Ryser's permanent formula.2. Alon's Permanent Lemma.3. Alon and Tarsi's Theorem about orientations and colorings of graphs.Furthermore, in combination with the Vigneron-Ellingham-Goddyn property of planar $n$-regular graphs, the formula contains as very special cases:4. Scheim's formula for the number of edge $n$-colorings of such graphs.5. Ellingham and Goddyn's partial answer to the list coloring conjecture.

scholarly journals Simple Method for Estimating the Contribution of Neighbouring n-beam Interactions to Two-beam Structure Factors

1988 ◽  
Vol 41 (3) ◽  
pp. 469
Author(s):  
HJ Juretschke ◽  
HK Wagenfeld
Keyword(s):  
Experimental Determination ◽  
Structure Factor ◽  
Beam Structure ◽  
Simple Method ◽  
Experimental Configuration ◽  
Structure Factors ◽  
Special Cases ◽  
Better Than

Unless special precautions are taken, the experimental determination of two-beam structure factors to better than 1 % may include contributions from neighbouring n-beam interactions. In any particular experimental configuration, corrections for such contributions are easily carried out using the modified two-beam structure factor formalism developed recently (Juretschke 1984), once the full indexing of the pertinent n-beam interactions is known. The method is illustrated for both weak and strong primary reflections and its applicability in special cases, as well as for less than perfect crystals, is discussed.

scholarly journals Kinematic Synthesis of Tendon-Driven Manipulators with Isotropic Transmission Characteristics

1993 ◽  
Vol 115 (4) ◽  
pp. 884-891 ◽  
Author(s):  
Yeong-Jeong Ou ◽  
Lung-Wen Tsai
Keyword(s):  
Jacobian Matrix ◽  
Null Vector ◽  
Force Distribution ◽  
Force Transmission ◽  
Transmission Characteristics ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Structure Matrix ◽  
Applied Forces ◽  
Matrix Design

This paper presents a methodology for kinematic synthesis of tendon-driven manipulators with isotropic transmission characteristics. The force transmission characteristics, from the end-effector space to the actuator space, has been investigated. It is shown that tendon forces required to act against externally applied forces are functions of the structure matrix, its null vector, and the manipulator Jacobian matrix. Design equations for synthesizing a manipulator to possess isotropic transmission characteristics are derived. It is shown that manipulators which possess isotropic transmission characteristics have much better force distribution among their tendons.

Rational Design of Stimuli-Responsive Polymers Modified Nanopores for Selective and Sensitive Determination of Salivary Glucose

2019 ◽  
Vol 91 (21) ◽  
pp. 14029-14035
Author(s):  
Miao Yang ◽  
Chunrong Ma ◽  
Shushu Ding ◽  
Yujie Zhu ◽  
Guoyue Shi ◽  
...  
Keyword(s):  
Rational Design ◽  
Stimuli Responsive ◽  
Stimuli Responsive Polymers ◽  
Responsive Polymers ◽  
Sensitive Determination
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