2 Serial robot designs

In its most general form, a serial robot design consists of a number of rigid links connected with joints. Simplicity considerations in manufacturing and control have led to robots with only revolute or prismatic joints and orthogonal, parallel and/or intersecting joint axes (instead of arbitrarily placed joint axes). In his 1968 Ph.D. thesis, [55], Donald L. Pieper (1941–) derived a very practically relevant result:

Figure 1: A Kuka-160 serial robot.

Figure 2: A Staubli (formerly Unimation) “PUMA” serial robot.

Figure 3: The three motion capabilities of a spherical wrist. This terminology comes from the observation that the depicted wrist makes rotations about the , and axes of the subsequent joints.

This result had a tremendous influence on the design of industrial robots: until 1974, when Cincinnati Milacron launched its robot (which has three consecutive parallel joints, i.e., intersecting at infinity, Fig. 4), all industrial manipulators had at least one prismatic joint [78] (see e.g., [73] for an impressively large catalogue) while since then, most industrial robots are wrist-partitioned 6R manipulators, such as shown in Figures 1 and 2. These 6R robots have six revolute joints, and their last three joint axes intersect orthogonally, i.e., they form a spherical wrist such as, for example, the ZXZ wrist whose motion capabilities are illustrated in Fig. 3. Hence, they can achieve any possible orientation.

Figure 4: The Cincinnati Milacron serial robot.

Figure 5: An Adept SCARA robot.

As Pieper proved, [55], this construction leads to a decoupling of the position and orientation kinematics, for the forward as well as the inverse problems. The inverse solution for the three wrist joints is a copy of the inverse Euler angle problem (discussed in another Chapter); the remaining three joints are then found by solving a polynomial of, at most, fourth order, whatever their kinematic structure is. The extra structural simplifications (i.e., parallel or orthogonal axes) introduced in the serial robots of, for example, Figures 1 and 2, lead to even simpler solutions (Sect. 8.2). (Intuitively speaking, each intelligently chosen geometric constraint imposed on the kinematic structure simplifies the calculations, because it reduces the solution search space.) The simplest kinematics are found in the SCARA (Selectively Compliant Assembly Robot Arm) design, Fig. 5. This design has three vertical revolute joint axes, and one vertical prismatic joint at the end. SCARA robots are mainly used for “pick-and-place” operations. In such a task, the robot must be stiff in the vertical direction (because it has to push things into other things) and a bit compliant in the horizontal plane, because of the imperfect relative positioning between the manipulated object and its counterpart on the assembly table. This desired selective compliance behaviour is intrinsic to the SCARA design; hence the name of this type of robots.

Hybrid designs. A last industrially important class of “serial” robot arms are the gantry robots, Fig. 6. They have three prismatic joints to position the wrist, and three revolute joints for the wrist. Strictly speaking, a gantry robot is a combination of a parallel translation structure with a serial spherical wrist. The parallel construction is very stiff (cf. metal cutting machines) so that these robots are very accurate. In large industrial applications (such as welding of ship hulls or other large objects) a serial manipulator is often attached to a two or three degrees of freedom gantry structure, in order to combine the workspace and dexterity advantages of both kinematic structures. (TODO: add a picture of the Nexus design: a 3 DOF parallel base on which a 3DOF spherical wrist is mounted.)

Figure 6: A gantry robot. (Only the first three prismatic degrees of freedom are shown.)

Figure 7: Notations used in the geometrical model of a serial kinematic chain.

Design characteristics. The examples above illustrate the common design characteristics of (most) industrial serial robot arms:

1. They are anthropomorphic, in the sense that they have a “shoulder,” (first two joints) an “elbow,” (third joint) and a “wrist” (last three joints). So, in total, they have the six degrees of freedom needed to put an object in an arbitrary position and orientation.
2. Almost all commercial serial robot arms have only revolute joints. Compared to prismatic joints, revolute joints are cheaper and give a larger dextrous workspace for the same robot volume.
3. Serial robots are very heavy, compared to the maximum load they can move without loosing their accuracy: their useful load to own-weight ratio is worse than 1/10! The robots are so heavy because the links must be stiff: flexible links cause deformations, and hence position and orientation errors at the end-point.
4. Simplicity of the forward and inverse position and velocity kinematics has always been one of the major design criteria for industrial manipulator arms. Hence, almost all of them have a very special kinematic structure, with a majority having the 321 design of Fig. 8. The special kinematic structures have efficient closed-form solutions because they allow for the decoupling of the position and orientation kinematics. The geometric feature that generates this decoupling is the intersection of joint axes.