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.
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).