Robotics and Automation (EPM4066) Tutorial 3 (Inverse Kinematics) 1. Consider the link-coordinate diagram for the four-axis cylindrical-coordinate robot with tool

roll motion as shown. Here the vector of joint variables is q , and

the kinematic parameters are given in the table below.

[ ]Tdd 4321 ,,, θθ=

y2 x2

z2

a) Find the arm matrix T . )(qtoolbase

b) Solve the inverse kinematics equations by finding (in wi. The base angle q . 1

ii. The vertical extension . 2qiii. The radial extension . 3qiv. The tool roll angle q . 4

The tool pose is given in form of a homogenous transf 2. Consider the link-coordinate diagram of the five-axis a

a4

Solve the inverse kinematics equations using a geometric, the shoulder angle q , the elbow angle q , the tool p

(in whichever order is easiest). The tool pose is

transformation matrix.

1q

5q2 3

Axis θ d a α home 1 q1 0 0 0 0 2 π/2 q2 0 π/2 d 3 0 q3 0 π/2 r 4 q4 d4 0 0 π

hichever order is easiest):

ormation matrix.

rticulated robot Rhino XR-3:

d5

approach by finding the base angle itch angle and the tool roll angle

given in form of a homogenous 4q