代做TRC4800/MEC4456 Robotics PC 3: Inverse Kinematics代写C/C++语言

Department of Mechanical and Aerospace Engineering

TRC4800/MEC4456 Robotics

PC 3: Inverse Kinematics

Objective: To solve inverse kinematics problem and gain insight of the multi-solution problem.

Problem 1. As shown in Figure 1, a 2-DOF positioning table is used to orient parts for arc-welding. The forward kinematics that locate the bed of the table (Link 2) with respect to the base (Link 0) are

Given an arbitrary unit direction fixed in the frame. of the bed (Link 2), , derive the inverse kinematics solution for θ1 and θ2, such that this  vector is parallel with the z-axis of the base frame, or . Note that there may be multiple solutions for each angle. Is there a case where a unique solution cannot be found (i.e. singular condition)?

Figure 1: The 2-DOF positioning table

Problem 2. Derive the inverse kinematics solutions for the three-link manipulator shown in Figure 2(a), when

1. the target transformation matrix  is given

2. the target position of an end effector positioned  in Frame. F3, is given in Frame. F0 as 

The DH parameter of the manipulator are as follows

Figure 2: The manipulators for Problems 2 (LHS) and 3 (RHS)

Problem 3. A 3-DOF manipulator is shown in Figure 2(b), consisting of two revolute joints and a single prismatic joint with the base plate fixed to the ground. Derive the inverse kinematics solutions for a given arbitrary location and orientation

The DH parameters of the manipulator are

Problem 4.

Figure 3: Planar Robot for Problem 4.

The transformation matrcies between the base and tool frames are:

Note: Your answers should reflect use of these transformation matrices, or otherwise the correct  generated by the matrices above. Do not reassign frames and use a different set of matrices or they will be marked as incorrect.

1. Solve the inverse kinematics of the robot using the algebraic method; that is find equations for θ1, d2 and θ3 in terms of the arbitrary location and orientation of the end effector shown in 

2. If the transformation matrix relating the base and tool frames is:

Find all valid solutions for the joint variables, if one exists. Let L1 = 2 and L3 = 4, and assume d2 ≥ 0.