ECE 470: Introduction to Robotics Homework 2
Question 1. (12 marks)
A 4-DOF (excluding gripper) robotic serial manipulator arm is shown in Figure 1.
Using the D-H convention learned in class,
a) Assign frames to the links on a schematic diagram that represents the robot arm
b) Tabulate the D-H parameters
c) Obtain the forward kinematics representing the pose of end-effector frame {E}
referenced from base frame {0}.
Question 2. (8 marks)
The serial manipulator arm is tasked to write on the board plane Zo, with a pen
attached to the gripper {E}. For the ink to flow, 0Zpen has to be (0 0 -1)T
i.e. vertically
downwards. As shown in the diagram, axis XE and ZE are parallel to Zpen and Ypen.
respectively. The distance between ZE and Ypen is k0.
State any assumption or condition while working on the following:
a) Write down the transformation matrix 𝑝𝑒𝑛𝑇
𝐸
b) If the pen tip is to be place on the board with coordinates 0
(u,v), find the
expressions describing the joint variable q in terms of k0-4, u and v.
c) Describe the workspace of the writing task if the distance between ZE and Ypen is
now change to k0/2. Assume that q2 can only move its link in a range of 0 to 180
o
from the plane.
