Rafael Avilés

Dynamic analysis of plane mechanisms with lower pairs in basic coordinates

Abstract In this article, we shall present the numerical solution to the dynamic problem of planar mechanisms with lower pairs. This method is based on the basic coordinates and link constraints. We shall begin by describing the matrix formulation of the inertial forces on a link and creating the dynamic equilibrium equations in three different ways: in Lagrangian coordinates, generalized coordinates and coordinates with Lagrange Multipliers. Finally, some examples, obtained by numerical integration of the equations of movement, will be given of problems of evolution in time of the configuration of a mechanical system.

Computer method for kinematic analysis of lower-pair mechanisms—I velocities and accelerations

Abstract This work presents a new method for the analysis of lower pair mechanisms with the help of a computer. This method make use of the coordinates of the pairs and of those of other points of interest as Lagrangian coordinates of the problem. It also makes use of link constraint equations. Perhaps, the most attractive features of this method are its conceptual simplicity and the ease with which it can be programmed in a digital mini-computer. This work is divided into two parts. The first part describes the coordinates and constraint equations made use of, with emphasis on the analysis of velocities and accelerations. The second part presents the resolution of three typically non-linear problems: initial position, finite displacements, and static equilibrium position of a mechanism with elastic connections. It presents an iterative method of rapid convergence and demonstrates that a good initial estimate is not required.

A practical procedure to analyze singular configurations in closed kinematic chains

The authors present a general method for the automated singularity analysis of any mechanism at a given configuration. The procedure uses a base of the motion space. This is obtained from a velocity equation characterized by a geometric matrix. This special form of Jacobian matrix has some advantages for automatic implementation. This approach provides the degree of freedom associated with the singularity, uncontrolled motion, and kinematic dependencies. It also facilitates the choice of actuators and redundant devices. The method has been implemented in a computer program for kinematic analysis.

Computer method for kinematic analysis of lower-pair mechanisms—II position problems

Abstract In the first part of this study, a new method for solving the problem of kinematic analysis was presented, based on the concepts of “basic coordinates” and “link constraint equations”. In this second part, these same concepts are used to solve the problems of initial position, finite displacements and static equilibrium position of a mechanism with springs between its links. The proposed algorithms are elementary in their formulation and of exceptional efficiency in their performance. The methods describes are based on the solution of a problem of mathematical programming. Several examples are presented, giving an idea of the potential of said algorithms.

Judder vibration in disc brakes excited by thermoelastic instability

Friction vibrations and noises which are common in brakes, have attracted a great deal of attention lately. This paper analyses low frequency vibrations in disc brakes excited at high car speed. This vibration, called judder, has a frequency in the range 10 to 300 Hz and usually comes in association with hum noises. The dynamic phenomenon shows two principal components, one normal and the other one tangential to the disc brake surface. It is explained how variations of friction coefficient, and thermoelastic instability caused by the tangential component, contribute to the appearance of judder. A numerical analysis in 3D using the finite element method has been implemented combining both tangential and normal components, and solving the thermoelastic process. Special attention is dedicated to the simulation of the thermoelastic process showing the correlation with experiments.

Calculation of General Static Load-Carrying Capacity for the Design of Four-Contact-Point Slewing Bearings

This paper presents a calculation of the general static load-carrying capacity of four-contact-point slewing bearings under axial, radial, and tilting-moment loads. This calculation is based on a generalization of Sjovall and Rumbarger’s equations and provides an acceptance surface in the load space. This acceptance surface provides a solid basis to compute acceptance curves for the design and selection of bearings of this kind.

A fairly general method for optimum synthesis of planar mechanisms

Abstract This article introduces a new method for optimum synthesis of planar mechanisms with lower pairs. The method uses a single objective function for any mechanism and for any type of synthesis, making it possible to perform even mixed syntheses. It is also possible to consider a wide variety of constraints and initial conditions. The error minimization process is carried out on two levels, and techniques which have been proved efficient for the problem under consideration are described. Finally, the article presents several examples which have been solved by the proposed method.

Kinematic analysis of mechanisms via a velocity equation based in a geometric matrix

In this paper, a geometrical approach is proposed to obtain a velocity equation valid for planar and spatial linkages. This equation is formed by a so called geometric matrix, and it can be found in a general and systematic way easily implemented in computer software. This procedure grants a direct inference of a kinematic property for velocities in linkages with the same topology and identical link orientation. In addition to this, a method is proposed to obtain the instantaneous degree of freedom of a mechanism in any position via the application of the geometric matrix. This also conveys a series of considerations on the detection and analysis of singular configurations. An indicator of the proximity to singularities is proposed and vectors of the motion space are found to analyse the type of singularity.

A method for the study of position in highly redundant multibody systems in environments with obstacles

This paper looks at a method for the analysis of highly redundant multibody systems (e.g., in the case of cellular adaptive structures of variable geometry) in environments with obstacles. Our aim is to solve the inverse kinematics in successive positions of multibody systems, avoiding the obstacles in its work environment. The multibody systems are modeled via rod-type finite elements, both deformable and indeformable, and the coordinates of their nodes are chosen as variables. The obstacles are modeled via a mesh of points that exert repulsive forces on the nodes of the model of the multibody, in order to model the obstacle avoidance. Such forces have been chosen inversely proportional to the Nth power of the distance between the corresponding points of the obstacle and of the multibody system. The method is based on a potential function and on its minimization using the Lagrange Multiplier Method. The solution of the resulting equations is undertaken iteratively with the Newton-Raphson Method.

A finite element approach to the position problems in open-loop variable geometry trusses

The present paper looks at some kinematic and static-equilibrium problems that arise with variable-geometry trusses (VGTs). The first part of the paper looks at the use of active controls in the correction of static deformations, the second part at the position problems. The separation between deformable- and rigid-body displacements makes it possible to consider separately the corrections in each component of the structure. VGTs are considered as open-loop linkages with redundant rigid-body degrees of freedom. Owing to this redundancy, possible solutions to the inverse problem are in general infinite, for which reason it is necessary to use some optimization criteria. To tackle the problem an optimization procedure with constraints is developed for the purpose of minimizing the displacements of the actuators. Suitable use of the constraints allows us to solve the direct position problem using the same optimization procedure.