COMPOSITE MECHANISMS

All machines are composed of simple mechanisms____gears, cams, linkages, belts, chains, Geneva wheels, and so on. For instance, an automobile is the assemblies of a power plant, power transmission, steering gear, running gear, braking system, differential, and the rest. Nearly all the assemblies are composed of the simple mechanisms listed above. Not only automobiles, but also machine tools, sewing machines, type writers, automatic assembly lines, and those assembled together for special purposes. They can be either a novel invention or a harmonic engineering system. However, these machines are not the subjects we are concerned with. The subjects which we would study are called Composite Mechanisms___ geared linkages, cam-link mechanisms, cam-gear mechanisms, chained linkages, and their combinations. Not all the machines come from composite mechanisms. The purpose of studying composite mechanisms is to improve the characteristics and functions of common mechanisms. Since composite mechanisms originate from simple mechanisms; they are easy to be manufactured and assembled, and cheap in cost. Along with the reasonable design, they may be smooth, harmonic, noiseless, shockless and can be efficiently operated. Certainly, the research of composite mechanisms should not be restricted in planar mechanisms; further more, it should not be only one degree of freedom. However, planar composite mechanisms with freedom of one degree have been studied most, consequently the achievement is great. In this book, planar composite mechanisms with one degree of freedom are to be studied mainly. Studying mechanisms is for designing mechanisms. Design in mechanism field is called synthesis. Since analysis is the premise of synthesis; the more is analyzed, the easier is synthesized. We would do more work in analysis than that in synthesis. And the synthesis is just the dimensional synthesis*. The synthesis of planar composite mechanism has two methods___the graphical and the analytical. The former is based on kinematic geometry dealing with finitely separate positions and infinitesimally close positions of planar configurations or kinematic planes. It needs the knowledge of algebraic curves, differential geometry, projective geometry and so on. Therefore, it seems as a difficult job to be handled, especially for the engineers who are not familiar with theoretical mechanisms. The latter needs iterative method with computer programming to solve the problems. It may be tedious though. The fundamental knowledge of vector, complex numbers, matrix , differential equations, and high order algebraic equations is required only. It is welcome for its simplicity and popularity. Besides, being an auxiliary means of analytical method, primary graphical approaches which do not belong to the category of such puzzled classical geometry is adopted. It just involves the basic geometrical axioms and theorems. Owing to its simplicity and clarity, it can guide the way for problem solving and check the analytical computing results. The analytical method with the graphical means as its cooperator will play an important role in the study of composite mechanisms in this text. Finally, We should know that the composition of simple mechanisms was a reality as ancient as, before Christ in China, the south-pointing chariot (composition of different gear trains) shown in Fig.0.1; and in eighteenth century in England, the Watt’s steam engine (composition of epicyclic gear train and linkages) shown in Fig.0.2. All machines are composed of simple mechanisms____gears, cams, linkages, belts, chains, Geneva wheels, and so on. For instance, an automobile is the assemblies of a power plant, power transmission, steering gear, running gear, braking system, differential, and the rest. Nearly all the assemblies are composed of the simple mechanisms listed above. Not only automobiles, but also machine tools, sewing machines, type writers, automatic assembly lines, and those assembled together for special purposes. They can be either a novel invention or a harmonic engineering system. However, these machines are not the subjects we are concerned with. The subjects which we would study are called Composite Mechanisms___ geared linkages, cam-link mechanisms, cam-gear mechanisms, chained linkages, and their combinations……………… Not all the machines come from composite mechanisms. The purpose of studying composite mechanisms is to improve the characteristics and functions of common mechanisms. Since composite mechanisms originate from simple mechanisms; they are easy to be manufactured and assembled, and cheap in cost. Along with the reasonable design, they may be smooth, harmonic, noiseless, shockless and can be efficiently operated. Certainly, the research of composite mechanisms should not be restricted in planar mechanisms; further more, it should not be only one degree of freedom. However, planar composite mechanisms with freedom of one degree have been studied most, consequently the achievement is great. In this book, planar composite mechanisms with one degree of freedom are to be studied mainly. Studying mechanisms is for designing mechanisms. Design in mechanism field is called synthesis. Since analysis is the premise of synthesis; the more is analyzed, the easier is synthesized. We would do more work in analysis than that in synthesis. And the synthesis is just the dimensional synthesis*. The synthesis of planar composite mechanism has two methods___the graphical and the analytical. The former is based on kinematic geometry dealing with finitely separate positions and infinitesimally close positions of planar configurations or kinematic planes. It needs the knowledge of algebraic curves, differential geometry, projective geometry and so on. Therefore, it seems as a difficult job to be handled, especially for the engineers who are not familiar with theoretical mechanisms. The latter needs iterative method with computer programming to solve the problems. It may be tedious though. The fundamental knowledge of vector, complex numbers, matrix , differential equations, and high order algebraic equations is required only. It is welcome for its simplicity and popularity. Besides, being an auxiliary means of analytical method, primary graphical approaches which do not belong to the category of such puzzled classical geometry is adopted. It just involves the basic geometrical axioms and theorems. Owing to its simplicity and clarity, it can guide the way for problem solving and check the analytical computing results. The analytical method with the graphical means as its cooperator will play an important role in the study of composite mechanisms in this text. Finally, We should know that the composition of simple mechanisms was a reality as ancient as, before Christ in China, the south-pointing chariot (composition of different gear trains) shown in Fig.0.1; and in eighteenth century in England, the Watt’s steam engine (composition of epicyclic gear train and linkages) shown in Fig.0.2.