R2. Kinematics

• Find homogenous transformations for an RRR robot:

Assume the link lengths are, respectively, 2, 1 and 1.

• For selected joint angles plot coordinate systems associated with each joint.
• Assume q₁=q₂=q₃=0. What are expected positions and orientations of coordinate systems? What is expected translation vector in robot kinematics? What is expected rotation?
• Calculate the kinematics for the joint values from the previous item. Is the result the same as expected?
• For the same joint angles calculate Euler angles from kinematics transformation. Check the result with the expected value.

• To report:
  1. Write homogenous transformations for each joint and kinematics for the joint angles q₁=0, q₂=π/4, q₃=-π/6. Include Matlab code used to obtain these matrices.

  2. Find the joint angles for which the translation vector of the kinematics is [0,1,3].

• Define an RT robot using toolbox functions. Verify its D-H parameters.

>> import ETS3.*
>> rob=SerialLink([Revolute('d',1,'alpha',pi/4) Prismatic('a',1)])
>> rob.name='RT'

• Calculate kinematics for given joint angle and translation and plot the result

>> rob.fkine([pi/4 1])

• To report:
  1. Use toolbox function to define the robot from task 1.
  2. Include code.

• Find D-H parameters for the Kuka KR16 industrial robot presented below.
• Calculate kinematics for selected joint angle values.
• To report:
  1. Include a matrix of D-H parameters
  2. Include a vector of joint angles and kinematic matrix calculated for it.