This exercise focuses on DH parameters and the forward (position and orientation) kinematics
transformation for the planar 3-DOF, 3R robot shown below. The following fixed-length
parameters are given: 1 = 4, 2 = 3, 3 = 2 ( )
a) Derive the DH parameters. You can check your results against what we derived in class.
b) Derive the neighboring homogeneous transformation matrices 1
, = 1, 2, 3. These are
functions of the joint-angle variables , = 1 , 2 , 3. Also, derive the constant 3
by
inspection: The origin of { } is in the center of the gripper fingers, and the orientation of
{ } is always the same as the orientation of {3}.
c) Use Symbolic MATLAB to derive the forward kinematics solution 3 0
and 0
symbolically
(as a function of
). Abbreviate your answer, using = sin
, = cos
, and so on.
Also, there is a ( 1 + 2 + 3) simplification, by using sum-of-angle formulas, that is due
to the parallel axes. Calculate the forward kinematics results (both 3 0
and 0
) via
MATLAB for the following input cases:
i) 1 = 0, 2 = 0, 3 = 0
ii) 1 = 10°, 2 = 20°, 3 = 30°
iii) 1 = 90°, 2 = 90°, 3 = 90°
For all three cases, check your results by sketching the manipulator configuration and
deriving the forward kinematics transformation by inspection. (Think of the definition of
ENGR 486/586 Robot Modelling and Control
2020 Winter 1 Due: 11:59 pm, Thursday, November 19
0
in terms of a rotation matrix and a position vector.) Include frames { }, {3}, and
{0} in your sketches.
Notes:
In your report (.pdf file), write the answer to each part (e.g., (b)) separately and include the
codes related to that part after the results of that part in your report. Then, write the results
and codes of the next part (e.g., (c)).
In addition to your .pdf report, submit your .m file(s) separately too.
