Errors in Constant-Velocity Shaft Couplings

Shaft couplings with an odd number of joints are modeled with rotation matrices such that the transmission plane in which the axis of the central joint moves can be arbitrarily specified. It is shown that when the transmission plane coincides with the homokinetic plane, the mechanism functions as a constant velocity coupling, otherwise it does not. The cyclic variation in output speed, which occurs when the constant-velocity criteria is not met, is quantified and the results enable the design engineer to predict performance of constant-velocity couplings when deviation from ideal geometry occur because of manufacturing and installation tolerances or wear.

A Model of the Human Spine: Forward and Inverse Kinematics

The human spine is a sophisticated mechanism consisting of 24 vertebrae which are arranged in a series-chain between the pelvis and the skull. By careful articulation of these vertebrae, a human being achieves fine motion of the skull. The spine can be modeled as a series-chain with 24 rigid links, the vertebrae, where each vertebra has three degrees-of-freedom relative to an adjacent vertebra. From the studies in the literature, the vertebral geometry and the range of motion between adjacent vertebrae are well-known. The objectives of this paper are to present a kinematic model of the spine using the available data in the literature and an algorithm to compute the inter vertebral joint angles given the position and orientation of the skull. This algorithm is based on the observation that the backbone can be described analytically by a space curve which is used to find the joint solutions..

Using Constraint Management Techniques to Design Spur and Helical Gears

This paper presents the use of constraint management techniques to design spur and helical gears. The constraints for gear design are presented in a declarative manner such that they can be incorporated in a general Design Shell environment. A declarative representation allows the designer to experiment with a number of different designs and perform “what-if” scenarios. Since spur gears form a subset of helical gears, the mathematical formulation is presented for helical gears only. The analysis of helical gears is based on the AGMA/ANSI Standard 2001-B88.

Design of an Epicyclic Transmission for Speed Control of a Turbine-Generator System

An improved speed control method is proposed for a turbine-generator system. Whereas the present method employs a steam valve to control the flow of steam according to the desired output, the proposed system uses an epicyclic gear train to provide fine control of the speed, while coarse control is still maintained through the steam valve. The systematic design of such a gear train is the objective of this project. Two configurations are considered as suitable candidates. After the transmissions are analyzed to obtain the speed and torque relations, the dynamic equations of motion and control equations for the systems are derived for simulation purposes. The simulations are then conducted for various load cases and parameter values to determine a suitable design for application in the power industry. The final configuration allows constant generator output speeds to be reliably maintained in the face of significant load disturbances.

Complete Balancing of Linkages Using Complete Dynamical Equivalents of Floating Links: CDEL Method

Partially dynamically equivalent link concept has been used for partial shaking force balancing of the slider-crank mechanisms of engines for a long time. The article offers methods of forming complete dynamically equivalent link (CDEL) for floating binary, ternary, and quaternary links by which a mechanism can be completely balanced eliminating shaking force and shaking moment. Developments and applications are simple. Four-bar and slider-crank mechanisms, Walt’s and Stephenson’s type six-bar mechanisms and some eight-bar mechanisms are completely balanced to illustrate different forms of CDEL in different mechanisms. CDEL uses auxiliary masses and mass moments of inertia on a floating link. The use of the auxiliary masses is illustrated in numerical examples. A Watt’s type body guiding six-bar mechanism interacting with a robot is completely balanced in an application example.

The Creation of a Multi-Link Load Balancing Mechanism for Planetary Gearing: Part 2 — Optimum Mechanism Selection and Dimension Determination

This paper is the second of a series of two papers which designed a new type of load balancing mechanisms for planetary gearings with arbitrary number of planets. In this paper the common expression of the non-uniform load share factor was deduced, and a function parameter:force-arm factor and their solution was given. That makes it possible that the dimensions and the ability of load equilibrium of Multi-Link Load Balancing Mechanisms can be determined. The criteria of optimum load balancing Mechanisms selection were set up with consider of the effects of turning pair clearances, and optimum mechanisms were selected among the 15 candidates obtained in Part 1. Finally, it was demonstrated that the optimum multi-link load balancing mechanisms for arbitrary number of planets had the similar topological structures and same function and performence of load equilibrium.

Bidirectional Extreme Convergency Methods (BECM) to Identify the Mobility Regions of the RSSR Mechanism

The BECM are proposed to classify spatial four-link mechanisms according to groups such as crank-rocker, double-rocker and double-crank (drag link). The BECM can determine the feasible regions and number of the extreme values exactly and solve them simply without complex derivation and calcultion. The paper concerns itself mainly with the RSSR linkage but it can be applied also to other types such as RSSP, RSCP, RSCR etc. The method is very simple and the geometric concept is very clear. Although the graphical methods is mainly introduced in this paper, certainly, it can also be coded in computer to solve out their accurate values.

An Analytical Method for Locating Velocity Instantaneous Centers

An analytical method is presented for locating all velocity instantaneous centers of linkage mechanisms with single or multiple degrees of freedom. The method is based on the fact that the coefficient matrix of the derived velocity equations for vector loops, independent inputs, and instantaneous centers is singular. This approach also works for special cases with kinematic indeterminacy or singular configurations.

Balancing Conditions for Planar Mechanisms

One of the problems of the complete inertia force and moment balancing of planar mechanisms consists of the deriving from the so-called balancing conditions. In recent publications on this field these balancing conditions are seperately derived for each particular mechanism [1], [2], [3]. In the present paper a new method is presented which derives the balancing conditions for planar mechanisms with an arbitrary structure (except for mechanisms containing cam pairs) in generality. This algorithm is suitable for the application of computer algebra systems.

Kinematic Analysis and Synthesis of Three-Input, Eight-Bar Mechanisms Driven by Relatively Small Cranks

Approximate kinematic equations are developed for the analysis and design of three-input, eight-bar mechanisms driven by relatively small cranks. Application of a method in which an output link is presumed to be comprised of a mean and a perturbational motions, along with the vector loop approach facilitates the derivation of the approximate kinematic equations. The resulting constraint equations are, (i) in the form of a set of four nonlinear equations relating the mean link orientations, and (ii) a set of four linear equations in the unknown perturbations (output link motions). The latter set of equations is solved, symbolically, to obtain the output link motions. The approximate equations are shown to be effective in the synthesis of three-input, small-crank mechanisms.