This assignment is to develop trajectory for a Three-Link Planar Robotic Arm, sh
ID: 1770946 • Letter: T
Question
This assignment is to develop trajectory for a Three-Link Planar Robotic Arm, shown in Figure 1. The link parameters of the robot are shown in Figure 1, as well as the world coordinate frames. All the joints are revolute joints. Based on the parameters shown in Table 1, 1) Construct the coordinate frames and draw the home (initial) configuration of the robot. 2) Find the coordinate transformation matrices and derive the forward kinematics of the robot. 3) Solve the inverse kinematics, (i.e., given a configuration of the end effector, find the joint 4) Give matrix T in closed form angles). Write the Jacobian transformation matrix The purpose of trajectory planning is to create the joint space desired trajectories that are needed to realize a given task. The output is going to be fed to the motion tracking controller for execution. 5) The required motion is a straight line between the initial point P [0.711, 0.2244, 0] (meters) and thefinal point Pf= [0.6179, 0.3203, 0)" (meters). Task requirements specify that the end-effector frame has the constant orientation, ie. the orientation angle is to be constant during the entire motion and is set to 4-54°. Note that = 1 + 2 + 3. The shape of the cartesian trajectory should be a straight line. The initial and final cartesian velocities and accelerations should be zero. The total motion time is t = 4sec. The shape of the cartesian linear acceleration along the line connecting the initial and final trajectories is given as a function of time in Figure 2. Plot the joint angle, velocity, and acceleration trajectories corresponding to the above motion. Draw the initial and final configurations of the robot with dimensions and angles shown. 6) 7)Explanation / Answer
This project research has been supported by the National Science
Centre, Poland. Project's objectives:
1. Design of the Lagrange Jacobian inverse
2. Elaboration of dynamically consistent Jacobian inverses
3. Development of trajectory planning Jacobian algorithms
4. Design of motion planning and control algorithms for parallel non-holonomic manipulators
5. Development of dedicated software framework