Week 4 Project - Simple Crank Mechanism

Question 1

Simulate the simple crank mechanism using cylinders (diameter = 2m) in a 2D plane (XY) as shown in the figure below

In the case shown above, Revolute joints are located at P0 and P1, What type of joint must be given at P2 (Joint C) so that the system doesn't have redundancy issues?

NOTE: Joint C is a type of joint that will perform translational motion only along the X-axis (Basically Joint C is the slider of the crank-slider mechanism)

Also, prove why the joint you have selected will be the ideal joint for the system using DOF calculations, also, what type of joint is this?

Ideally, after you have selected the perfect joint for Joint C to reproduce the desired motion, what will be the final DOF of this system? also, validate with calculations

Solution:

Checking units and changing the acceleration due to gravity orientation

Required points are created

Required bodies are created, and the properties will later be associated to the graphic of the cylinder respectively

cylinder graphics are created with 2 as diameter.

Required revolute joints are created.

DOF:

Joint C should be an inline joint, in order for the model to be a kinematic model.

DOF:

The inline joint (DOF=2) restricts the motion in only translation directions thus giving the net DOF of the system as O. Thus, the system will not have any redundancy issues.

For instance, if we select a revolute joint:

DOF of one rigid body = 6

DOF of two rigid bodies = 6 x 2 = 12 ........(1)

DOF removed by one revolute joint = 5

DOF removed by three revolute joints = 5x3 =15 ........ (2)

DOF of the system (1)-(2) = 12-15 = -3

Now, if we select an inline joint:

DOF of one rigid body = 6

DOF of two rigid bodies = 6 x 2 = 12 .......(1)

DOF removed by two revolute joints=5 x 2 = 10

DOF removed by one inline joint = 2

DOF removed by all joints = 10 + 2 = 12...... (2)

DOF of the system (1) - (2) = 12 - 12 = 0

Thus, the inline joint selected will be ideal for the system.

Question 2

After selecting joint C, simulate the following mechanism with initial angular velocity at the joint in P0 as 0.5 rad/sec (for mass and inertial properties obtain from associated geometry)

Now, plot a graph for velocity vs time on Joint C or Point P2 w.r.t the ground

Find the maximum velocity of Point P2 w.r.t the ground

What is the DOF of the system now and why?

Solution:

Enabling the angular velocity for the first revolute joint.

Required outputs are requested using the outputs functionality

Plot:

DOF:

The DOF of the systems remains unchanged (i.e. O) as it depends on the alterations in motions, couplers or joints. By inducing a velocity, the DOF of the system will not get affected.

The same is validated below. Go to Tools - Check Model - DOF to check the details of our model.

Question 3

Now, suppress the initial angular velocity, and apply a load of 1000 KN on P1 and simulate and answer the following questions

Now, plot a graph for the reaction torque vs time at P0 and explain your results

Compare the range of motion of the crank mechanism between this case and the previous case and explain the reason for the difference if any

Solution:

Required force is applied at the revolute joint

Required output are requested

plots: 

Reaction torque is zero because it is not constrained at joint 0.

Range of motion:

case 1: with angular vel

case 2: with 1000kN force

Question 4

Now, in the same case as Question 3 create a BISTOP function at point P0 with range (-10,0) degrees

Now, again, plot a graph for the reaction torque vs time at P0 and explain your results

A screenshot of the entire interface must be attached with the plot for all the simulated cases.

Solution:

New Force is applied at point 0 which contains bitstop expression to limit the motion

Required output are requested using Vtorq function.

Plot:

the reactive torque is shown above.