Appendix A

The following are the 12 kinematics equations for RRP:RRR manipulator. These kinematic equations ar simplified by Maple. (The rest of Appendix A is not included)

Transformation Matrix for RRP : RRR with(linalg):

a1:=a1;

a2:=a2;

a3:=a3;

a4:=0;

a5:=0;

a6:=0;

d1:=d1;

d2:=d2;

d3:=d3;

d4:=0;

d5:=0;

d6:=d6;

alpha1:=alpha1;

alpha2:=alpha2;

alpha3:=alpha3;

alpha4:=-Pi/2;

alpha5:=Pi/2;

alpha6:=0;

theta1:=theta1;

theta2:=theta2;

theta3:=theta3;

theta4:=theta4;

theta5:=theta5;

theta6:=theta6;

A1:=matrix([[cos(theta1),-sin(theta1)*cos(alpha1),sin(theta1)*
sin(alpha1),a1*cos(theta1)],[sin(theta1),cos(theta1)*cos(alpha1),
-cos(theta1)*sin(alpha1),a1*sin(theta1)],[0,sin(alpha1),cos(alpha1),d1]
,[0,0,0,1]]);

The next 12 nonlinear equations should be solved to find out the Inverse Kinematics of the Manipulator;

e11:=simplify(AA[1,1]);

e21:=simplify(AA[2,1]);

e31:=simplify(AA[3,1]);

e12:=simplify(AA[1,2]);

e22:=simplify(AA[2,2]);

e:32=simplify(AA[3,2]);

e13:=simplify(AA[1,3]);

e23:=simplify(AA[2,3]);

e33:=simplify(AA[3,3]);

dx:=simplify(AA[1,4]);

dy:=simplify(AA[2,4]);

dz:=simplify(AA[3,4]);