Robot Arm Modeling - Kinematics

by Lee Farrell

Submitted : Fall 2009

Kinematics is the science of motion. In a two-joint robotic arm, given the angles of the joints, the kinematics equations give the location of the tip of the arm. Inverse kinematics refers to the reverse process. Given a desired location for the tip of the robotic arm, what should the angles of the joints be so as to locate the tip of the arm at the desired location? There is usually more than one solution and can at times be a difficult problem to solve. This is a typical problem in robotics that needs to be solved to control a robotic arm to perform tasks it is designated to do. In a 2-dimensional input space, with a two- joint robotic arm and given the desired co-ordinate, the problem reduces to finding the two angles involved. The first angle is between the first arm and the ground (or whatever it is attached to). The second angle is between the first arm and the second arm. Let theta1 be the angle between the first arm and the ground. Let theta2 be the angle between the second arm and the first arm (Refer to Figure 1 for illustration). Let the length of the first arm be L1 and that of the second arm be L2. Let us assume that the first joint has limited freedom to rotate and it can rotate between 0 and 90 degrees. Similarly, assume that the second joint has limited freedom to rotate and can rotate between 0 and 180 degrees. (This assumption takes away the need to handle some special cases which will confuse the discourse). Now, for every combination of theta1 and theta2 values the x and y coordinates are deduced using forward kinematics formulae. Generate x and y coordinates values for all combinations of theta1 and theta2 values using the trigonometric equations and plot them on a graph. This can be achieved by using trigonometric values to calculate the x-y position of the tip of the arm. You can assume a step size of 1 degree and L1 as 10 and L2 as 5. All units can be in inches.

[ Back ]