Given a 5 degree of freedom manipulator below establish the

Given a 5 degree of freedom manipulator below, establish the orthogonal coordinate frames and complete the parameter table.

This is a 5 d.o.f manipulator. Base has 1 dof

Shoulder 1 dof

elbow 1 dof

wrist 2 dof

Problem is to write the tables in terms of the parameters for each frame. The frames are set up as follows:

It is called the Denavit Hartenberg representation:

1. Number the jonts from 1 to 5 starting from the base and ending with the tool, with yaw, pitch roll .

Assign a RH orthogonal coordinate frame to the base making Zo align with the axis of the first joint.

Align Z1 with the axis of the next joint, and so on.

Select X1 to be orthogonal to both Z0 and Z1. Next select Y1 to be a RH orthonoral frame L1.

Proceed to the next joint.

Compute Theta k as the angle of rotation from Xk-1 to Xk measured about Zk-1

Measure Bk as the distance between Xk and Xk-1 axes and a common normal.

Compute Dk as the distance from origin of frame LK-1 to the point Bk measured along Zk-1

Compute Ak as the distance from point Bk to the origin of frame Lk measured along Xk.

Compute alpha k as the angle of rotation from Zk-1 to Zk measured about Xk

repeat for all joints.

This is the DH algorithm

TABLE is:

theta d a alpha

1 theta 1 8.1 0 -90

2 theta 2 0 7 0

3 theta 3 0 7 0

4 theta 4 0 0 -90

5 theta 5 3.8 0 0