objects in the environment。

FIGURE 1。6: Kinematic equations describe the tool frame relative to the base frame

as a function of the joint variables。

FIGURE 1。7: For a given position and orientation of the tool frame, values for the

joint variables can be calculated via the inverse kinematics。

FIGURE 1。8: The geometrical relationship between joint rates and velocity of the

end-effector can be described in a matrix called the Jacobian。

3、Symbol

Symbol is always the problems in science and engineering。 In this book, we use the following convention:

First: Usually, uppercase variables vector or matrix。 Scalar lowercase variables。

Second：Tail buoy use (such as the widely accepted) indicating inverse or transposed matrix。论文网

Third：Tail buoy not subject to strict conventions, but may be that the vector components (for example, X, Y, Z) or can be used to describe the PBO / P in a position of the bolt。

Fourth：We will use a lot of trigonometric function, we as a cosine symbol angle E1 can adopt the following methods: because the E1 = CE1 = C1。

In the vector sign note general: many mechanics textbook treatment number of vector at a very abstract level and often used vector is defined relative to expression in different coordinate systems。 The most obvious example is, in addition to vector is relative to a given or known a different frame of reference。              This is usually very convenient, resulting in compact structure, elegant formula。 For example, consider the angular velocity, connected in series with the last body ° W4 'four rigid body (such as the manipulator links) relative to the fixed seat chain。 Due to the angular velocity vector addition, angular velocity equation at last link we can write a very simple vector:

However, unless the information is relative to a common coordinate system, they cannot be concluded, therefore, although elegant, equation (1。1) calculation。 Most of the "work"。 A case study of the manipulator, such statements, (1。1) work coordinate system hidden bookkeeping, which is often we need to practice。 Therefore, in this book, we put the symbol reference frame vectors, we don't and carrier, unless they are in the same coordinate system。 In this way, we derive expressions for computing numerical solution, "bookkeeping" problem can be directly applied to the actual。

Summary

The robot is a typical electromechanical integration device, it uses the latest research results of machinery and precision machinery, microelectronics and computer, automation control and drive, sensor and information processing and artificial intelligence and other disciplines, with the development of economy and all walks of life to the automation degree requirements increase, the robot technology has been developing rapidly, the emergence of a variety of robotic products。 The utility of robot products, not only can solve many practical problems difficult to solve by manpower, and the promotion of industrial automation process。 At present, the research and development of robot relates to many aspects of the technology, the complexity of system structure, development and development cost is generally high, limiting the application of the technology, to some extent, therefore, the development of economic, practical, high reliability of robot system with a wide range of social significance and economic value。 Based on the design of mechanical structure and drive system, the kinematics and dynamics of the cleaning robot is analyzed。 Kinematics analysis is the basis of path planning and trajectory control of the manipulator, the kinematics analysis, inverse problem can complete the operation of space position and velocity mapping to drive space, using the homogeneous coordinate transformation method has been the end of manipulator position and arthrosis transform relations between the angle, geometric analysis method to solve the inverse kinematics problem of manipulator, provides a theoretical basis for control system design。 The robot dynamics is to study the relationship between the motion and force of science, the purpose of the study is to meet the need of real-time control, this paper use straightaway language introduced the related mechanical industrial robots and control knowledge for us, pointing the way for our future research direction。 Robot is a very complicated learning, in order to go into it, you need to constantly learn, the road ahead is long, I shall search。