In Denavit-Hartenberg (DH) notation, rigid manipulator links define the spatial relationship between axes of neighboring joints.
engineering
Description
Trajectory Simulation for a 5-DoF
Manipulator
Background and Objective
In
Denavit-Hartenberg (DH) notation, rigid manipulator links define the spatial
relationship between axes of neighboring joints. Four DH parameters (qi,
di, ai, ai)
represent the pose (position and orientation) of the i-th link with
respect to the link i-1 of a serial manipulator. This representation of
the pose is in the form of the following transformation matrix:
|
For a revolute
joint, qi is the joint variable and di
is constant;
the other way around for a prismatic joint (di
is the joint variable). The
parameters ai and ai
are constant. The objective of
this experiment is to apply such systematic methodology to the direct kinematic
problem of finding the end-effector’s pose for an input vector of joint
variables.
Task Description
a.
Assign DH parameters for the
manipulator indicated in Figure 1 (the dimensions a1–a7
are all in the same plane whereas a8 is perpendicular to that plane). Expected outcome: tabulated DH parameters.
b.
With the end-effector in the
origin of the 5th frame, show the trajectory of this point in the base
frame (index 0) if all joints are moving concurrently at some (any) constant
rate over p (3.14) radians for each rotary, joint and 1 unit for each prismatic,
joint. In other words, trace the said point as it moves in space during the
motion of all joints. Expected outcome: plots like those of Figure 2 and
program listing in ASCII characters (not as an image).
c.
Find coordinates of the
end-effector in the base frame of reference when all rotary joints have moved by
37 degrees and all prismatic joints have moved by 0.34 units (report values).
Much of this lab is probably best done in MATLAB,
which can be downloaded free of charge through CityU-Portal. Please do not use the robotics toolbox
of MATLAB for the above listed three tasks of this lab (students are welcome to
experiment with that toolbox, for example for the inverse kinematic problem for
the same manipulator). The use of other programing languages based on English
keywords and alphabet is permitted (but not advisable). A sample program is
included with this lab-sheet; it has been supplemented with many comments to
assist the process of learning MATLAB (MATLAB provides extensive online help).
