Solving a system of equations with multiple solutions

Hi everyone,

I am having a problem that I have to solve 2 equations with 3 variables, which means that there will be mutiple solutions. My 2 equatons are:

cos(theta1)*sin(theta3 - pi/2) + cos(theta3 - pi/2)*sin(theta1) + d2*cos(theta1) - 2 = 0
sin(theta1)*sin(theta3 - pi/2) - cos(theta1)*cos(theta3 - pi/2) + d2*sin(theta1) = 0

And the variables are theta1, theta3, d2. I am sure that there will be expressions that show the relation between these variables. But I dont know how to find them?

Answer 1

[Birdman]

syms theta1 theta3 d2
eqn1=cos(theta1)*sin(theta3-pi/2)+cos(theta3-pi/2)*sin(theta1)+d2*cos(theta1)-2==0;
eqn2=sin(theta1)*sin(theta3-pi/2)-cos(theta1)*cos(theta3-pi/2)+d2*sin(theta1)==0;
sol=solve(eqn1,eqn2);
%%the solutions are found in terms of d2
sol.theta1
sol.theta3

[Tuan Hua]

Thanks, that is a perfect answer. Could I expand the problem? Actually, I have a system of equations for robot inverse kinematics in which there are 3 equations. So, for general, how can I solve the problem?

[Birdman]

I prefer using geometric approach for inverse kinematics but, the solution changes depending on the complexity of the robot.

[Tuan Hua]

I agree that the solutions for inverse kinematics problem are very complex. There is any tools in Matlab deals with this problem?

[Birdman]

http://petercorke.com/wordpress/toolboxes/robotics-toolbox

[Tuan Hua]

Thanks for the link.