Design and Control of a Pantograph Robot

Overview

The goal of this project was to design and build a 2-DOF Pantograph Robot. The user would be able to specify and X and Y location for the end point of the pantograph, along with different paths that the robot arm could take. The basic circuit design and computer code was taken from the High Speed Motor Control project and adapted to work with our robot design.

Kinematics

The kinematics for our robot design were derived from The Pantograph Mk. II - A Haptic Instrument. The forward and inverse kinematics as used in the MATLAB program are shown below, along with a diagram showing how the reference frames are defined in our setup.

Forward Kinematics

x2 = L1 * cos(theta);
y2 = L1 * sin(theta);

y4 = L4 * sin(alpha);
x4 = L4 * cos(alpha) - L5;

two_to_four = sqrt((x2-x4).^2 + (y2-y4).^2);

two_to_h = (L2^2 - L3^2 + two_to_four.^2) ./ (2 * two_to_four);

yh = y2 + (two_to_h./two_to_four).*(y4-y2);
xh = x2 + (two_to_h./two_to_four).*(x4-x2);

three_to_h = sqrt(L2^2 - two_to_h.^2);

x3 = xh + (three_to_h./two_to_four) .* (y4-y2);
y3 = yh - (three_to_h./two_to_four) .* (x4-x2);