1.1 KINEMATICS
• A robot must be able to map between things that it can control, such as joint angles, to the position of the tool in space.
• Describing the position of the robot in terms of joint positions/angles is Joint Space.
• Real space is often described with a number of coordinate systems,
- cartesian
- polar
- spherical
• Positions can also be specified with respect to the robot base (Robot Coordinates), or globally (World Coordinates).
1.1.1 Basic Terms
• Robot base coordinates don’t move and are often used to specify robot tool position and orientation. (centre of the robots world)
• Link/Joint Coordinates - specify where joints, endpoints or centers are located.
• Tool coordinates - determine where the tool is and what orientation it is in.
• World Coordinates - relates various robots to other robots and devices.
• Coordinate transformation - Can map from one set of coordinates to another. Most common method is matrix based. One special case of this is the Denavit-Hartenrberg transformation.
1.1.2 Kinematics
• Forward kinematics involves finding the endpoint of the robot (xT, yT) given the joint coordinates (theta1, theta2)
• There a number of simple methods for finding these transformations,
- basic geometry
- transformation matrices
- Denavit-Hartenberg transformations
1.1.2.1 - Geometry Methods for Forward Kinematics
• For simple manipulators (especially planar ones) this method is often very fast and efficient.
• The method uses basic trigonometry, and geometry relationships.
• To find the location of the robot above, we can see by inspection,
• The problem with geometrical methods are that they become difficult to manage when more complex robots are considered. This problem is overcome with systematic methods.
1.1.2.2 - Geometry Methods for Inverse Kinematics
• To find the location of the robot above, we can see by inspection,
• Mathematically this calculation is difficult, and there are often multiple solutions.
