J. Angeles – författare

1. 1 Preliminary Concepts A cam mechanism is a mechanical system consisting of three basic components: a driving element, called the cam; a driven element, termed the follower; and a fixed frame. Sometimes, an intermediate element is introduced between the cam and the follower with the purpose of improving the mechanism performance. This element is called the roller because function is to produce a pure-rolling relative motion be­ tween the cam and the follower. The purpose ofa cam mechanism is the transmission of power or information. In applications concerning power transmission, the main good to be transmitted is force or torque; in applications ofinformation transmission, the main good transmitted takes the form of motion signals. Most modern appli­ cations of cam mechanisms, to be described shortly, are of the former type. Cam mechanisms used for information transmission were traditionally found in measuring instruments. With the advent ofmodern microprocessor-based hardware, this typeof application is becoming less common. Nevertheless, cam mechanisms are still used in a wide spectrum of applications, especially in automatic machines and instruments, textile machinery, computers, printing presses, food-processing equipment, internal combustion engines, control systems, and photographic equipment (Prenzel, 1989). In the design of cam mechanisms, the engineer performs several activities, namely, task definition, synthesis, analysis, optimization, and dynamic simulation. These tasks do not always follow this order. In fact, some loops may appear in the foregoing tasks, such as those illustrated in Fig. 1. 1. 1.

This volume provides an account of developments in computational kinematics. Included are both numerical computations and symbolic manipulations. The volume reports on trends and progress in a broad class of problems, and the information is collated into six parts describing the main themes: (i) kinematic algorithms, whereby general kinematic problems are discussed in light of their solution algorithms; (ii) redundant manipulators; (iii) kinematic and dynamic control, in which the link between kinematics and the disciplines of dynamics and control is highlighted; (iv) parallel manipulators; (v) motion planning, touching on computational geometry; and (vi) kinematics of mechanisms, describing the closed kinematic chains. The volume contains a representative sample of current techniques available for kinematics problems. It should be of interest to researchers, graduate students and practising engineers engaged in work relating to kinematics, robotics, machine design and computer science.

Three main disciplines in the area of multibody systems are covered: kinematics, dynamics, and control, as pertaining to systems that can be modelled as coupling or rigid bodies. The treatment is intended to give a state of the art of the topics discussed.

The aim of this book is to provide an account of the state of the art in Com­ putational Kinematics. We understand here under this term ,that branch of kinematics research involving intensive computations not only of the numer­ ical type, but also of a symbolic nature. Research in kinematics over the last decade has been remarkably ori­ ented towards the computational aspects of kinematics problems. In fact, this work has been prompted by the need to answer fundamental question­ s such as the number of solutions, whether real or complex, that a given problem can admit. Problems of this kind occur frequently in the analysis and synthesis of kinematic chains, when finite displacements are considered. The associated models, that are derived from kinematic relations known as closure equations, lead to systems of nonlinear algebraic equations in the variables or parameters sought. What we mean by algebraic equations here is equations whereby the unknowns are numbers, as opposed to differen­ tial equations, where the unknowns are functions. The algebraic equations at hand can take on the form of multivariate polynomials or may involve trigonometric functions of unknown angles. Because of the nonlinear nature of the underlying kinematic models, purely numerical methods turn out to be too restrictive, for they involve iterative procedures whose convergence cannot, in general, be guaranteed. Additionally, when these methods converge, they do so to only isolated solu­ tions, and the question as to the number of solutions to expect still remains.

Despite advances in robot technology, in which industrial manipulators have replaced mechanisms, cam mechanisms still find important industrial applications in the textile, food processing and manufacturing industries. This book is a modern, up-to-date treatise on the important subject of cam synthesis.Cam mechanisms have been studied from different points of view, namely, kinematic synthesis, dynamic synthesis, analysis, design, optimization and manufacturing. This book is oriented to the kinematic synthesis of cam mechanisms in a unified framework, i.e. that spatial, spherical and planar cam mechanisms are integrated in the same formulation. Traditionally, the synthesis of the three types of cam mechanisms has been approached using independent formulations. With a unified formulation, both well known types of cam mechanisms, as well as novel cam mechanisms can be synthesized, as shown in the book. Moreover, since all the design parameters are considered in a unified framework, the optimization theory of cam mechanisms can be applied systematically, i.e. the criteria applied for the optimization of planar cam mechanisms, which can be found to some extent in the literature, can be complemented in order to provide general criteria for the optimization of spherical and spatial cam mechanisms.The underlying philosophy of the book has been to exploit sound mathematical and kinematical tools of analysis and synthesis that could be used only with the available current software and hardware.The approach and tools introduced in this book can assist the designer in producing a broad spectrum of mechanisms than those described in the book.This will be an invaluable reference for engineering designers.

1. 1 Preliminary Concepts A cam mechanism is a mechanical system consisting of three basic components: a driving element, called the cam; a driven element, termed the follower; and a fixed frame. Sometimes, an intermediate element is introduced between the cam and the follower with the purpose of improving the mechanism performance. This element is called the roller because function is to produce a pure-rolling relative motion be­ tween the cam and the follower. The purpose ofa cam mechanism is the transmission of power or information. In applications concerning power transmission, the main good to be transmitted is force or torque; in applications ofinformation transmission, the main good transmitted takes the form of motion signals. Most modern appli­ cations of cam mechanisms, to be described shortly, are of the former type. Cam mechanisms used for information transmission were traditionally found in measuring instruments. With the advent ofmodern microprocessor-based hardware, this typeof application is becoming less common. Nevertheless, cam mechanisms are still used in a wide spectrum of applications, especially in automatic machines and instruments, textile machinery, computers, printing presses, food-processing equipment, internal combustion engines, control systems, and photographic equipment (Prenzel, 1989). In the design of cam mechanisms, the engineer performs several activities, namely, task definition, synthesis, analysis, optimization, and dynamic simulation. These tasks do not always follow this order. In fact, some loops may appear in the foregoing tasks, such as those illustrated in Fig. 1. 1. 1.

Despite advances in robot technology, in which industrial manipulators have replaced mechanisms, cam mechanisms still find important industrial applications in the textile, food processing and manufacturing industries. This book is a modern, up-to-date treatise on the important subject of cam synthesis. Cam mechanisms have been studied from different points of view, namely, kinematic synthesis, dynamic synthesis, analysis, design, optimization and manufacturing. This book is oriented to the kinematic synthesis of cam mechanisms in a unified framework, i.e. that spatial, spherical and planar cam mechanisms are integrated in the same formulation. Traditionally, the synthesis of the three types of cam mechanisms has been approached using independent formulations. With a unified formulation, both well known types of cam mechanisms, as well as novel cam mechanisms can be synthesized, as shown in the book. Moreover, since all the design parameters are considered in a unified framework, the optimization theory of cam mechanisms can be applied systematically, i.e. the criteria applied for the optimization of planar cam mechanisms, which can be found to some extent in the literature, can be complemented in order to provide general criteria for the optimization of spherical and spatial cam mechanisms. The underlying philosophy of the book has been to exploit sound mathematical and kinematical tools of analysis and synthesis that could be used only with the available current software and hardware. The approach and tools introduced in this book can assist the designer in producing a broad spectrum of mechanisms than those described in the book. This will be an invaluable reference for engineering designers.

1. 1 Preliminary Concepts A cam mechanism is a mechanical system consisting of three basic components: a driving element, called the cam; a driven element, termed the follower; and a fixed frame. Sometimes, an intermediate element is introduced between the cam and the follower with the purpose of improving the mechanism performance. This element is called the roller because function is to produce a pure-rolling relative motion be­ tween the cam and the follower. The purpose ofa cam mechanism is the transmission of power or information. In applications concerning power transmission, the main good to be transmitted is force or torque; in applications ofinformation transmission, the main good transmitted takes the form of motion signals. Most modern appli­ cations of cam mechanisms, to be described shortly, are of the former type. Cam mechanisms used for information transmission were traditionally found in measuring instruments. With the advent ofmodern microprocessor-based hardware, this typeof application is becoming less common. Nevertheless, cam mechanisms are still used in a wide spectrum of applications, especially in automatic machines and instruments, textile machinery, computers, printing presses, food-processing equipment, internal combustion engines, control systems, and photographic equipment (Prenzel, 1989). In the design of cam mechanisms, the engineer performs several activities, namely, task definition, synthesis, analysis, optimization, and dynamic simulation. These tasks do not always follow this order. In fact, some loops may appear in the foregoing tasks, such as those illustrated in Fig. 1. 1. 1.