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Basic knowledge of the theory of machines and mechanisms: This field studies the structure and motion of mechanisms within machines, as well as the structure, forces, mass, and motion of machines themselves. People generally refer to institutions and machines together as machinery. A mechanism is a combination of two or more components connected in a movable manner to achieve a specified motion. A machine is composed of one or more mechanisms, and is used to perform useful work or to convert mechanical energy into other forms of energy. The main components of this discipline are mechanism theory and mechanical dynamics. Different machines are often composed of a limited number of common mechanisms; for example, the main mechanism in internal combustion engines, compressors, and punching machines is all a crank-slider mechanism. The motion of these mechanisms differs from that in general mechanics; it depends only on their geometric constraints, and not on the forces acting on them, the mass of the components, or time. In 1875, F. Leroi of Germany separated these common problems from general mechanics, wrote the book \"Theoretical Kinematics,\" and established the foundations of mechanism theory. Many of the concepts, ideas, and research methods proposed in the book are still in use today. In 1841, R. Willis of Britain published \"Principles of Mechanics\". Since the mid-19th century, mechanical dynamics has also gradually taken shape. Entering the 20th century, the theory of machinery emerged, which combined the study of mechanism theory with mechanical dynamics. In 1934, the book \"Principles of Machinery\" written by Liu Xianzhou of China was published. In 1969, the International Association for Institutions and Principles of Machines was established in Poland, abbreviated as IFTOMM. The subject of study in mechanism theory are various common mechanisms found in machines, such as link mechanisms, cam mechanisms, gear mechanisms, screw mechanisms, and mechanisms for intermittent motion (such as ratchet mechanisms and gear racks), as well as composite mechanisms. Its research focuses on the principles underlying the structure of mechanisms and the determinism of their motion, as well as the motion analysis and synthesis of mechanisms. Mechanics, when studying the motion of mechanisms, approaches it from a purely geometric perspective, without considering the effect of forces on motion. The subject of study in mechanical dynamics is machines or combinations of machines. The research focuses on determining the actual motion laws of machines under known forces, as well as issues such as regulation, friction and mechanical efficiency, and the balance of inertial forces. Following the traditional approach to mechanical principle research, gaps between the contact surfaces of components, the elasticity of components or thermal deformation, as well as errors caused by manufacturing and assembly, are generally not taken into account. This is generally feasible for machinery operating at low speeds. However, as machinery evolves toward higher speeds and greater precision, it is also necessary to study the motion changes caused by the aforementioned factors. Thus, starting from the 1940s, the issue of institutional accuracy was raised again. Due to the rapid development of aerospace technology, as well as manipulators and industrial robots, the issue of mechanism precision has received increasing attention and has become an essential part of the principles of mechanics