John M. Hansen

Synthesis of Mechanisms Using Time-Varying Dimensions

Many methods of performing mechanism synthesis rely on an attempt to redefine the dimensions of the system in such a way that a deviation from the desired behavior is minimized by the use of optimization methods. During the optimization process the optimizer may, however, suggest values of the dimensions, or design variables, that lead to infeasible designs, i.e. dimensions for which the mechanism cannot be assembled in one or more positions.With the method proposed her, this problem is overcome by allowing the dimensions to vary during the motion of the system and subsequently minimizing the deviation of each variable dimension over a cycle. That is, for each time step the dimensions are allowed to change in order to obtain assembly as well as a desired kinematic behavior. This will lead to a variation of each dimension during a cycle of the mechanism, and this variation is the objective that is sought minimized. The minimization problem is solved using the optimality criterion.

Synthesis of Spatial Mechanisms Using Optimization and Continuation Methods

The aim of this work has been to develop a method that can be used within synthesis of spatial mechanisms, specifically on the problem of designing a mechanism for which a coupler point can describe a given path, given by a number of discrete points.

AN EFFICIENT METHOD FOR SYNTHESIS OF MECHANISMS USING AN OPTIMIZATION METHOD

The objective here is to design a mechanism so that a tracer point follows a given curve during a portion of the working cycle. To quantify a proposed design, the deviation between the desired curve the tracer point trajectory is measured. A gradient based optimization procedure is used to minimize this deviation. The design sensitivity analyses are efficiently computed using the direct differentiation method. The joint coordinate method is used to analyze the mechanisms. This formulation is advantageous because superfluous variables are eliminated from the planar analysis.

An Efficient Method for Synthesis of Planar Multibody Systems Including Shape of Bodies as Design Variables

A point contact joint has been developed and implemented in a joint coordinate based planar multibody dynamics analysis program that also supports revolute and translational joints. Further, a segment library for the definition of the contours of the point contact joints has been integrated in the code and as a result any desired contour shape may be defined. The sensitivities of the basic physical variables of a multibody system, i.e., the positions, velocities, accelerations and reactions of the system with respect to the automatically identified independent design variables may be determined analytically, allowing design problems where the shape of the bodies are of interest to be handled in both a general and efficient way.

Synthesis of Mechanisms

In this chapter the focus will be on synthesis of mechanisms. Part of the material is based on the papers (Hansen, 2002, 2000; Jensen and Hansen, 2005) from which some of the figures are taken. In the chapter some methods are described that are not commonly used within the area, and to understand them requires some knowledge about general optimization methods. It is therefore recommended that this chapter is read after the other chapters in the volume which treat optimization and synthesis have been read.

Planar Multibody Systems

The first three chapters given here are actually divided into two logical parts: Chapter 1–2 and Chapter 3. The first two chapters introduce the general analysis methods and notation used in most of the remaining chapters, including the concept of Cartesian coordinates. It is therefore recommended to read these chapters first. The chapters are divided into the four components: Planar kinematics, planar dynamics, spatial kinematics, and spatial dynamics. It does, however, only treat systems of rigid bodies; in later chapters it is shown how the methods can be expanded to deal with flexible bodies. The notation used here is strongly based on the one found in (Nikravesh, 1988).

Spatial Multibody Systems

As for the planar case a set of coordinates are needed to describe position and rotation of the bodies in a spatial mechanical system in order to describe the kinematics. For the translational coordinates that is fairly straight forward, as it merely requires an extra Cartesian coordinate, z. Therefore the position vector r i for a body i becomes

A Roller Chain Drive Model Including Contact with Guide-bars

r_i = \left\{ {\begin{array}{*{20}c} x \\ y \\ z \\ \end{array} } \right\}_i