require the most sophisticated computer controllers and software development.
Application Area
Robot manipulators are often classified by application area into assembly and nonassembly robots. Assembly robots tend to be small and electrically driven with either revolute or SCARA geometries (described below). Typical nonassembly application areas are in welding, spray painting, material handling, and machine loading and unloading.
One of the primary differences between assembly and nonassembly applications is the increased level of precision required in assembly due to significant interaction with objects in the workspace. For example, an assembly task may require part insertion (the so-called peg-in-hole problem) or gear meshing. A slight mismatch between the parts can result in wedging and jamming, which can cause large interaction forces and failure of the task. As a result, assembly tasks are difficult to accomplish without special fixtures and jigs, or without controlling the interaction forces.
Geometry
Most industrial manipulators at the present time have six or fewer DOF. These manipulators are usually classified kinematically on the basis of the first three joints of the arm, with the wrist being described separately. The majority of these manipulators fall into one of five geometric types: articulated (RRR), spherical (RRP), SCARA (RRP), cylindrical (RPP), or Cartesian (PPP). We discuss each of these below in Section 1.3.
Each of these five manipulator arms is a serial link robot. A sixth distinct class of manipulators consists of the so-called parallel robot. In a parallel manipulator the links are arranged in a closed rather than open kinematic chain. Although we include a brief discussion of parallel robots in this chapter, their kinematics and dynamics are more difficult to derive than those of serial link robots and hence are usually treated only in more advanced texts.
1.2.2 Robotic Systems
A robot manipulator should be viewed as more than just a series of mechanical linkages. The mechanical arm is just one component in an overall robotic system, illustrated in Figure 1.6, which consists of the arm, external power source, end-of-arm tooling, external and internal sensors, computer interface, and control computer. Even the programmed software should be considered as an integral part of the overall system, since the manner in which the robot is programmed and controlled can have a major impact on its performance and subsequent range of applications.
Figure 1.6 The integration of a mechanical arm, sensing, computation, user interface and tooling forms a complex robotic system. Many modern robotic systems have integrated computer vision, force/torque sensing, and advanced programming and user interface features.
1.2.3 Accuracy and Repeatability
The accuracy of a manipulator is a measure of how close the manipulator can come to a given point within its workspace. Repeatability is a measure of how close a manipulator can return to a previously taught point. The primary method of sensing positioning errors is with position encoders located at the joints, either on the shaft of the motor that actuates the joint or on the joint itself. There is typically no direct measurement of the end-effector position and orientation. One relies instead on the assumed geometry of the manipulator and its rigidity to calculate the end-effector position from the measured joint positions. Accuracy is affected therefore by computational errors, machining accuracy in the construction of the manipulator, flexibility effects such as the bending of the links under gravitational and other loads, gear backlash, and a host of other static and dynamic effects. It is primarily for this reason that robots are designed with extremely high rigidity. Without high rigidity, accuracy can only be improved by some sort of direct sensing of the end-effector position, such as with computer vision.
Once a point is taught to the manipulator, however, say with a teach pendant, the above effects are taken into account and the proper encoder values necessary to return to the given point are stored by the controlling computer. Repeatability therefore is affected primarily by the controller resolution. Controller resolution means the smallest increment of motion that the controller can sense. The resolution is computed as the total distance traveled divided by 2n, where n is the number of bits of encoder accuracy. In this context, linear axes, that is, prismatic joints, typically have higher resolution than revolute joints, since the straight-line distance traversed by the tip of a linear axis between two points is less than the corresponding arc length traced by the tip of a rotational link.
In addition, as we will see in later chapters, rotational axes usually result in a large amount of kinematic and dynamic coupling among the links, with a resultant accumulation of errors and a more difficult control problem. One may wonder then what the advantages of revolute joints are in manipulator design. The answer lies primarily in the increased dexterity and compactness of revolute joint designs. For example, Figure 1.7 shows that for the same range of motion, a rotational link can be made much smaller than a link with linear motion.
Figure 1.7 Linear vs. rotational link motion showing that a smaller revolute joint can cover the same distance d as a larger prismatic joint. The tip of a prismatic link can cover a distance equal to the length of the link. The tip of a rotational link of length a, by contrast, can cover a distance of 2a by rotating 180 degrees.
Thus, manipulators made from revolute joints occupy a smaller working volume than manipulators with linear axes. This increases the ability of the manipulator to work in the same space with other robots, machines, and people. At the same time, revolute-joint manipulators are better able to maneuver around obstacles and have a wider range of possible applications.
1.2.4 Wrists and End Effectors
The joints in the kinematic chain between the arm and end effector are referred to as the wrist. The wrist joints are nearly always all revolute. It is increasingly common to design manipulators with spherical wrists, by which we mean wrists whose three joint axes intersect at a common point, known as the wrist center point. Such a spherical wrist is shown in Figure 1.8.
Figure 1.8 The spherical wrist. The axes of rotation of the spherical wrist are typically denoted roll, pitch, and yaw and intersect at a point called the wrist center point.
The spherical wrist greatly simplifies kinematic analysis, effectively allowing one to decouple the position and orientation of the end effector. Typically the manipulator will
