Robotic kinematics depends on the use of right handed cartesian frames of reference. Manipulator Geometry
A manipulator consists of two types of joints, connected by a link.
A link is a solid mechanical structure which connects two joints. The main purpose of a link is to maintain a fixed relationship between the joints at its ends. The last link of a manipulator has only one joint, located at the proximal end (the end closest to the base) of the link. At the distal end of this link (the end furthest away from the base) instead of a joint, there is usually a place to attach a gripper: a tool plate.
The common link configurations are shown below. Between the axes of the joints at the ends of any link there can be two degrees of translation and two degrees of rotation. These degrees of freedom are called the link parameters.
Type 1 link
The simplest link has two parallel revolute joints with no twist between the axes; the axes of the joints are parallel. Type 2 link
If one of the joints in a type 1 link is twisted about the centre line of the link by an angle , an extra degree of rotation is added. The twist angle is the angle that would exist between the joint axes if the joints were coincident, and it can be thought of as a rotation around the X axis. Thus, the type 2 link has one degree of translation and effectively two degrees of rotation. Type 3 link
In this link, the second type of revolute joint in introduced. If joint n in the type 1 link is rotated 90o degrees about the Y axis so that the Z axis is collinear with the centre line of the link, we have the link configurationa shown. The significant difference between this link and the previous two links is that the joint axes intersect, whereas in the type 1 and type 2 links they are parallel. In summary
The axes of the joints are always along the Z axis of the originating frame. The link axis is always along the X axis of the originating frame. The normal displacement between the two frame is given the symbol a. The twist angle between the two joint frames is given the symbol Joints
Two types of joints are commonly found in robots: revolute joints, and prismatic joints. Unlike the joints in the human arm, the joints in a robot are normally restricted to one degree of freedom, to simplify the mechanics, kinematics, and control of the manipulator.
Rotary or revolute joints
In the top two, the axis of the joint is coincident with the centre line of the link. In some designs it is normal to the distal link. This joint is often used as a waist joint. In the bottom, the axis of the joint is normal to the link. One common use of this joint is as an elbow joint. In both cases, a revolute joint is capable of one degree of rotation, the joint variable is the angle, and the joint axis is in the Z direction. Most revolute joints cannot rotate through a full 360° , but are mechanically constrained.
Linear or prismatic joints
A prismatic joint is a sliding joint, with the axis of the joint coincident with the centre line of the sliding link. Since any prismatic form can be used for the elements of a sliding pair, it does not have a specific axis (as a turning pair does) but merely an axial direction. Nevertheless, it is convenient to choose a centre line or axis as a basis for analysis.
As with the revolute joint, there are two basic configurations: the axis can be collinear with the preceding (fixed) link, or orthogonal to it. A prismatic joint provides one degree of translation, the joint variable is the distance d, and the joint axis is in the z direction. With both types of joints, there are several common configurations of the joint with respect to the links attached to it. Summary
The displacement between two links is along the Z axis and is given the...