• 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 - 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. - 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.