Robot Modeling and Control. Mark W. Spong

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 possess three DOF for position, which are produced by three or more joints in the arm. The number of DOF for orientation will then depend on the DOF of the wrist. It is common to find wrists having one, two, or three DOF depending on the application. For example, the SCARA robot shown in Figure 1.14 has four DOF: three for the arm, and one for the wrist, which has only a rotation about the final z-axis.

The arm and wrist assemblies of a robot are used primarily for positioning the hand, end effector, and any tool it may carry. It is the end effector or tool that actually performs the task. The simplest type of end effector is a gripper, such as shown in Figure 1.9, which is usually capable of only two actions, opening and closing. While this is adequate for materials transfer, some parts handling, or gripping simple tools, it is not adequate for other tasks such as welding, assembly, grinding, etc.

Figure 1.9 A two-finger gripper. (Photo courtesy of Robotiq, Inc.)

A great deal of research is therefore devoted to the design of special purpose end effectors as well as of tools that can be rapidly changed as the task dictates. Since we are concerned with the analysis and control of the manipulator itself and not in the particular application or end effector, we will not discuss the design of end effectors or the study of grasping and manipulation. There is also much research on the development of anthropomorphic hands such as that shown in Figure 1.10.

Figure 1.10 Anthropomorphic hand developed by Barrett Technologies. Such grippers allow for more dexterity and the ability to manipulate objects of various sizes and geometries. (Photo courtesy of Barrett Technologies.)

      1.3 Common Kinematic Arrangements

      There are many possible ways to construct kinematic chains using prismatic and revolute joints. However, in practice, only a few kinematic designs are commonly used. Here we briefly describe the most typical arrangements.

      1.3.1 Articulated Manipulator (RRR)

The articulated manipulator is also called a revolute, elbow, or anthropomorphic manipulator. The KUKA 500 articulated arm is shown in Figure 1.11. In the anthropomorphic design the three links are designated as the body, upper arm, and forearm, respectively, as shown in Figure 1.11. The joint axes are designated as the waist (z₀), shoulder (z₁), and elbow (z₂). Typically, the joint axis z₂ is parallel to z₁ and both z₁ and z₂ are perpendicular to z₀. The workspace of the elbow manipulator is shown in Figure 1.12.

Figure 1.11 Symbolic representation of an RRR manipulator (left), and the KUKA 500 arm (right), which is a typical example of an RRR manipulator. The links and joints of the RRR configuration are analogous to human joints and limbs. (Photo courtesy of KUKA Robotics.)

Figure 1.12 Workspace of the elbow manipulator. The elbow manipulator provides a larger workspace than other kinematic designs relative to its size.

      1.3.2 Spherical Manipulator (RRP)

By replacing the third joint, or elbow joint, in the revolute manipulator by a prismatic joint, one obtains the spherical manipulator shown in Figure 1.13. The term spherical manipulator derives from the fact that the joint coordinates coincide with the spherical coordinates of the end effector relative to a coordinate frame located at the shoulder joint. Figure 1.13 shows the Stanford Arm, one of the most well-known spherical robots.

Figure 1.13 Schematic representation of an RRP manipulator, referred to as a spherical robot (left), and the Stanford Arm (right), an early example of a spherical arm. (Photo courtesy of the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign.)

      1.3.3 SCARA Manipulator (RRP)

The SCARA arm (for Selective Compliant Articulated Robot for Assembly) shown in Figure 1.14 is a popular manipulator, which, as its name suggests, is tailored for pick-and-place and assembly operations. Although the SCARA has an RRP structure, it is quite different from the spherical manipulator in both appearance and in its range of applications. Unlike the spherical design, which has z₀ perpendicular