代做TRC4800/MEC4456 Robotics PC 10: Force Control代做留学生SQL 程序

Department of Mechanical and Aerospace Engineering

TRC4800/MEC4456 Robotics

PC 10: Force Control

Objective: To understand the basic concepts of force control in robotic manipulators.

Problem 1. Give the natural and artificial constraints present for the motion of a square peg, sliding into a square socket (Figure 1), such that the square peg is able to slide into the socket without jamming. Assume no friction forces.

Figure 1: A square peg inside a socket.

Problem 2. Give the natural and artificial constraints for the motion of uncorking a bottle of wine using a corkscrew.

Assume the corkscrew is already inserted and no friction or pressure forces are present. Sketch your definition of {C}.

Problem 3. Give the natural and artificial constraints for the task of uncorking a bottle of champagne by hand.

Assume the cork is being held in the bottle by pressure and friction forces. Additionally apply a twisting moment to the cork. Give all the constraints using the same frame {C} from problem 2.

Problem 4. Give the natural and artificial constraints for the task of closing a hinged door with a manipulator. Make any reasonable assumptions needed. A sketch of the system is shown in Figure 2.

Figure 2: Robot closing door

Problem 5. Given

If the force-torque vector at the origin of {A} is

Find the 6 x 1 force-torque vector with reference point at the origin of {B}.

Problem 6. Derive the error-space equation for the system

Whose control law is

Hence, show that it is only possible to critically damp the system if the environmental stiffness (ke  ) is known.

Use the following equations and ζ to determine stability.

Where D refers to disturbances.