Robot Geometry
The study of robot kinematics, require a unified methodology to identify the variables of a robot's or manipulator's joints and links.
Co-ordinate Frames
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.
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
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Co-ordinate Frames
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.
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
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