Structural Configurations of Manipulators 1 In this homework, I have given information about the basic structural configurations of the manipulators with the concerned illustrations. 1) The Manipulator The manipulator is the mechanical unit which performs the movement function in the robot. It consists of a series of mechanical links and joints capable of producing controlled movement in various directions. The manipulator is composed of the main frame (the arm) and the wrist, each having three degrees of freedom, or axis of motion. Structurally, the robots can be classified according to the coordinate system of the main frame: Cartesian: three linear axes Cylindrical: two linear and one rotary axes Spherical: one linear and two rotary axes Jointed (Articulated): three rotary axes Robot motions, analogously to human motions, can be distinguished as global, regional, and local. Global Motion: This motion involves travel along distances that exceed the overall dimensions of the manipulator (e.g., wheeled motions along the track). Regional Motion: This motion provides placement of an end effector into various points of the workspace. Local Motion: This motion covers displacements of an end effector that are commeasurable with its dimensions, e.g., orientations in a given point or a small area of workspace, minor adjustments, travel of gripper jaws, etc. Accordingly, a robot structure can be divided in most of the cases into two substructures with distinct functions: the arm proper performs regional motions and is sometimes called the major linkage, and the wrist with an end effector or gripper executes local motions and is sometimes called the minor linkage. To move and orient a body in three dimensional-space, a mechanism should have at least six degrees of freedom: three to execute regional motions by the arm (to bring the end effector into a prescribed point) and three to execute local motions by the wrist (to properly orient the end effector at its final location). The seventh degree of freedom might be required for another local motion, the gripping action inside the end effector or gripper. In actual designs, the workspace is usually truncated because of the interference of structural elements, limitations of joint motions, singularities, etc. In order to aid in defining the coordinate system, a symbolic notation is used to describe the type and number of each joint, starting from the base to the end of the arm. Linear joints can be sliding or prismatic, designated as S and P respectively, and revolute joints, designated as R. By this notation, the spherical robotic arm, for example, would be called an RRP arm, and the jointed (or articulated) one an RRR arm. Possible kinematic configurations of three-jointed robot manipulators is seen in figure 1. One of the most important performance characteristics of a manipulator is the shape of its reach envelope, or its work volume. The shape of the work volume depends on the coordinate system, and its size depends on the dimensions of the robot arm. It should be noted that when a gripper or another tool
is attached to the wrist, the work volume exceeds the one given by the robot manifacturer, and this should be taken into account when planning for the safety of the people working near the robot. 2 The various configurations of robotic arms, their corresponding work volumes, their advantages and shortcomings to each other are discussed below. 2) Basic Structural Configurations An important consideration for the manipulator design is the selection of its coordinate frame. The most widely used frames are cartesian (rectangular), cylindrical, spherical, and jointed ( articulated ). 2.1) Cartesian Coordinate Robots ( Rectangular Frame Robots): Robots whose arms are moving in the rectangular or cartesian frame are used for relatively simple applications, such as loading and unloading production machinery and also for high-precision assembly and inspection operations. The arm is moving up and down (z direction) and also is travelling with the carriage and the cross beam (bridge) along the guideways (x and y directions), figure 2. Rectangular frame robots are the easiest to program because of the complete independence of their joint coordinates. For the same reason, there is no coupling between motions in all three axes; thus, it is relatively easy to control unwanted oscillations. Some disadvantages of the rectangular system are the difficulty to protect linear sliding surfaces; a need for a substructure to support the guideways, which increases the weight and limits the work zone; and a need to use long sliding bearings (or short bearings placed far apart) to reduce reactions and friction forces. It is relatively easy to achieve high speed and positioning accuracy in such manipulators, but the structure is relatively large and bulky in comparision with its work zone and can not be used in situations in which access inside enclosed areas is required (e.g., inside a car body). Figure 2 Figure 1
If the robot s end point has to trace a straight path of l length units in a velocity V, the axial velocities are; 3 V x = ( x / l )V V y = ( y / l )V V z = ( z / l )V l = ( x 2 + y 2 + z 2 ) 1/2 And x, y, and z are the components of l in the X, Y, and Z directions, respectively. Such simple relationships are not valid for other coordinate systems, for which complex computer algorithms are reqired to drive the end effector along straight-line trajectories. The controlling computers of these robots usually must transform the cartesian coordinates, in which most robotic task programs are written, to the coordinates associated with the joints of the manipulator. 2.2) Cylindrical Coordinate Robots: The main frame of cylinrical coordinate robots consist of a horizontal arm mounted on a vertical column which, in turn, is mounted on a rotary base, as shown in figure 3. The horizontal arm moves in and out, the carriage moves up and down on the column, and these two units rotate as a unit on the base. Thus the working volume is a cylindrical annular space. Figure 3 shows an actual cylindrical coordinate frame robot design. Arm 1 with gripper 2 is translated in horizontal (radial) and vertical directions and is rotated with column 3. The gripper (wrist) has only one orietation motion: rotation around the Figure 3 longitudinal axis of the arm (roll). Wrists with not more than two degrees of freedom (rotations around the longitudinal axis and around an orthogonal horizontal axis) are frequently used for robots with cylindrical coordinate frames since angular orientation of the arm in the vertical plane does not change. One disadvantage of the cylindrical frame robots is their reduced work zone. The arm can not reach below the bed of the structure. However, there are some ways to alleviate this shortcoming. One of them is shown in figure 4. The wrist provides three rotations, 4, 5, and 6, but the joint 4 for rotation around the horizontal axisis located relatively close to the vertical axisof the robot, thus providing for a substandial extention in up and down directions. Here, the wrist degrees of freedom for local motions are used, partly, as duplicates of the main structural degrees of freedom for regional motions. Figure 4
The disadvantage is that good dynamic performance is usually difficult to achieve in robots which contain a rotary base, The torque which the base motor has to supply depends on the position, speed, and acceleration of the other joints, and this causes variations in the reflected torque and moment of inertia. The moment of inertia reflected at the base depends not only on the weight of the object being carried but also upon the distance between the base axis and the manipulated object. This distance is a function of the instantaneous position of the gripper and the other joints during the motion. As a result, the effective moment of inertia at the base drive generally varies with time or position, which consequently results in inferior dynamic performance of the arm. 2.3) Spherical Coordinate Robots: The kinematic configuration of spherical, or polar, coordinate robot arms is similar to the turret of a tank. It consists of a rotary base, an elevated pivot, and a telescoping arm which moves in and out as shown in figure 5. The magnitude of rotation is usually measured by incremental encodes mounted on the rotary axes. The design of the spherical coordinate robots are usually quite complicated and require more sophiticated control systems, but they have the advantage of servicing a larger workspace. They constitude about 13% of the robot population. The disadvantage of spherical robots compared with their cartesian counterparts, is that there are two axes with relatively low resolution that varies with the arm length. The advantage of spherical robots over the cartesian and cylindrical ones is a better mechanical flexibility, the pivot axis in the vertical plane permits access to points at base level or below it. 2.4) Articulated Robots (Jointed Robots): 4 Articulated robots consist of three rigid members connected by two revolute joints and mounted on a rotary base shown in figure 6. This kinematic arrangement closely resembles that of a human arm. The gripper is analogous to the hand, which attaches to the forearm via the wrist. The elbow joint connects the forearm and the upper arm, and the shoulder joint connects the upper arm to the base. Sometimes a rotary motion in the horizontal plane is also provided at the shoulder joint. The shoulder rotates around the vertical axis (waist). The part is oriented by rotations of wrist in pitch (rotate), yaw (flex), and roll (hand) directions. Figure 5 Figure 6
5 The main advantage of the jointed configuration manipulators, which they share with the spherical coordinate manipulators, is the small size of the required hardware and of the floor space for their installation in comperation with the workspace. In addition to this, jointed robots demonstrate a very high degree of accessability; they could easily be programmed to perform manipulations in enclosed spaces. Another advantage of jointed manipulators is the elimination of sliding joints and, accordingly, guideways. All rotary bearings are easy to seal, they are mass produced as standart components, and they have low inertia and very low friction loses. Jointed robot structures have a lower required joint force (torque) as well as lower energy consumption. There are also the shortcomings of the jointed robots such as the degenerating behaviour of the arm near the workspace boundries. Another design shortcoming is associated with the fact that in conventional jointed robot axes of shoulder and elbow joints are parallel and orthogonal to the waist axis. Such a configuration is associated with a large workspace, but it has a relatively low stiffness for, practically, all directions of force acting on the end point. Accordingly, accuracy and repeatability of such systems, although reasonably good (up to ±0.2 mm), is not adequate for many precision assembly operations. Another significant disadvantage of the jointed configuration is a need to move the lower arm (elbow joint) motor when the upper arm or the waist is moving. Conventional motor-transmission units or direct drive motors are very heavy, thus they impair the system dynamics. One way to overcome this problem is to locate the motor close to a stationary base or on the base (waist) and to use a special light transmission system to transmit power to the shoulder joint. Despite all these disadvantages of the jointed robots, they can move at high speeds and has excellent mechanical flexibility, which make it the most common small and medium-sized robot.
6 Referances: 1) Eugene I. Rivin, Mechanical Design of Robots, McGraw-Hill Mechanical Engineering Series, 1988, pp. 13-30. 2) Yoram Koren, Robotics For Engineers, McGraw-Hill Industrial Engineering Series,1987, pp. 35-44. 3) Mark W. Spong, M. Vidyasagor, Robot Dynamics and Control, pp. 4-15. 4) C. Ray Asfahl, Robots and Manufacturing Automation, pp. 133-144. 5) Ben-Zion Sandler, Robotics, pp. 12-20.