代做TRC4800/MEC4456 Robotics PC 6: Dynamics 1代写C/C++程序

Department of Mechanical and Aerospace Engineering

TRC4800/MEC4456 Robotics

PC 6: Dynamics 1

Objective: To analyse the dynamics of a robotic through Lagrangian mechanics.

Problem 1. Derive the dynamic equations for the three-link manipulators shown in Figure 1 by means of Langrangian formulation. Assume only point masses (no inertia tensors, therefore no angular velocity component of K). Point masses, m1  and m2, lie at the middle-point of each link.

Figure 1: Planar RR Robot (left), Non-Planar RR robot (right)

Problem 2. Find the inertia tensor of a rigid cylinder of homogeneous density with respect to a frame with origin at the centre of mass of the body. Hints: Convert coordinates from Cartesian system (xyz) into a cylindrical system (r θ z). Formulas for changing the integration between sets of variables will be required.

Problem 3. For the robot in Figure 2, obtain the dynamics of the system using the Lagrangian method. Represent the dynamic equations in state-space (i.e. matrix) form. Assume that the centres of masses are point masses located midway along each link. Use the following transformation matrices:

Figure 2: Planar RP Robot