ECSE/CSCI 4480 Robotics I September 15, 2008
Homework # 3
Due: September 22, 2008
1. (60 points) Consider the four 3-DOF manipulators below. Find the forward kinematics
map (i.e., R0Tand p0Tin terms of θ1,θ2,θ3). Take the configuration shown as the zero
configuration. The origin of the tool frame is at the center of the gripper. Feel free to
use the MATLAB symbolic toolbox.
2. (40 points) Write a MATLAB function fwdkin.m that computes R0Tand p0Tfor a given
joint vector θ. The function should have the following input and output arguments:
function [R,p]=fwdkin(theta,type,H,P,n)
where theta is the input joint vector, type is the vector indicating the joint type (0
for rotational, 1 for prismatic, others may be added later), His a 3 ×nmatrix denoting
the axis of rotation in the zero configuration, Pis a 3 ×nvector denoting the link
vectors in the zero configuration, and nis the number joints.
The function should be able to accept either symbolic or numerical vectors theta.
Verify your result in Problems 1.
20 bonus points if you can implement fwdkin recursively (i.e., the function calls itself
repeatedly).
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