Group 11

Kinematics for a Trebuchet By: Alex Miller, Sun Chun Cheng, and Meagan Hughes

Introduction: We will be going over how to simulate the movement of a trebuchet within the

DMU Kinematics toolset in Catia. We will discuss how to make a mechanism capable

of being simulated. At the beginning of the tutorial you will be given a fully constrained

assembly which you will then edit or create joints in Catia and remove the degrees of

freedom that prevent the simulation. We will explain the concept of auto created joints

but we will not force you to go over the constraints of the trebuchet due to the potential

of an incorrect constraint that would make this tutorial inaccurate.

Objectives: To understand basic of Auto Joint Creations

To understand some of the many joints available in the

DMU Kinematics Workbench

To Simulate the movement of an assembly with a large

amount of parts

A brief introduction to the simulation with laws.

A working kinematics of a trebuchet

Open Folder Final, Open trebuchetassembly_final.CATProduct file.

Once the fully constrained assembly is open, start the DMU Kinematics. To do this go to start

Digital Mockup -> Kinematics.

Click on Assembly Constraints Conversion.

Click New Mechanism - Mechanism One

Click Auto Create

When you Auto Create joints the system takes the constraints that exist between your parts and

creates relationships between these parts. With a well-designed constraint system you can

remove degrees of freedom before going into the joint manipulation. I recommend designing

your constraints in such a way that it reduces the editing of the joints post creation.

The Unresolved Pairs should now read: 0/20.

These joints are determined by the degrees of freedom that exist between your parts due to

their constraints. So, one thing that one can do is restrict these degrees of freedom. Create

relationships between nonmoving joints and remove any ability for them to move. The

processes that we go through in this tutorial are removing these degrees of freedoms.

Later in this tutorial you will also create commands. Commands are driving movements so they

do not remove the degree of freedom but they will allow for the movement of these parts and

allow for simulation.

Moving forward in this tutorial it is important to understand the references underneath

the titles of joints are more important to which you should edit. When using a feature called

Auto Create Joints it will sometimes create the joints in a slightly different order.

Open Mechanism One DOF 7 in the tree. This is under Applications and then Mechanisms.

Open Joints in the tree underneath mechanisms.

The Parts that the joints are between is more important than the number of the joint.

Double click on Cylindrical.2 (MainAxis, Arm). Check Angle Driven

Double click on Cylindrical.2 (MainAxis, Arm) and make -277.2 lower limit and 0 upper limit.

Right click Cylindrical.4 (Weight Axis, Arm). Delete. Do not delete children

Select Rigid Joint from the toolbar.

Select Weight Axis and Arm for Part 1 and Part 1. This will replace Cylindrical 4.

Again it is more important you have the two parts that are part of the relationship then the

number.

Delete Cylindrical.6 (Axis sleeve, Part2.1). Do not delete children

Create a Rigid Joint between axis sleeve one and main axis

Delete cylindrical.11 (cap.1, Part2.1). Do not delete children

Delete Revolute 14. Do not delete children

Create a Rigid Joint between cap.2 and MainAxis.

Create Rigid joint for cap.1 and main axis.

Delete cylindrical 16 (leg right and mainaxis).

Create rigid joint between Leg right and main axis.

Double click on Cylindrical.19 (pin, Trough Base). Check angle driven and length driven

Double click on Cylindrical.19 (pin, Trough Base).

Make degree 0 and 180 and length 0 and 6(if it goes through instead of out change it to -6 to 0)

Set revolute.20 to angle driven. Again ensure that it is the joint between Weight and Weight

Axis.

Revolute.20 (Weight, Weight Axis) 0 to 277.2

The mechanism should now be capable of being simulated. What we have done is

removed the ability for any parts, outside of the parts that are desired to move, capable of

moving. Once this is complete Catia is capable of simulating the movement. The number of

commands that you create will be the number of parts capable of movement. When simulating

our trebuchet you will move the arm, weight and pin. Although there is a command for turning

the pin this movement is not necessary to our simulation although it is intended in the design.

Click on Simulation located in the toolbar.

Select Mechanism.1

Move Command.4 to opposite of end of starting position. Click Insert

Move Command.1 and 3 to opposite ends of starting position

Click Insert

Click Jump to Start

Change time step to .04

Play (ok)

Click on the Formulas button. We are now going to add formulas that control the movement of

the trebuchet. With correct formulas and understanding of the math behind the movements you

can simulate the movement of any object accurately and then take other measurements from

these movements.

Select Mechanism.1 DOF=0 in the Tree.

Click Mechanism.1\Commands\Command.1\Angle

Add Formula

Enter this as your formula =(-277.2deg)/(1s)*(Mechanism.1\KINTime)

What does this mean? This is the distance that the arm is going to travel per second over the

course of one run time. Mechanism.1\KINtime is one circuit of simulation. With that in mind one

is capable of applying mathematical measurements into the system and simulates accurate

movements.

As you can see the Active Column in the table now says yes in the row for

Mechanism.1\Commands\Command.1\Angle

Bear in mind that the number of the Command is determined by when they are created. What is

important to identify is that there are three Angle commands two of them belong to cylindrical

and so these are the only possible commands to be confused by. Check what joint each

command is related to. The only command that is unused is the Cylindrical Angle related to the

Pin.

Click Mechanism.1\Commands\Command.3\Angle

Add Formula

Enter this as your formula =(277.2deg)/(1s)*(Mechanism.1\KINTime)

Click Mechanism.1\Commands\Command.4\length

Add Formula

Enter this as your formula =(-3.2in)*(Mechanism.1\KINTime)/(.01s)

Under The Column Active in the three Rows that you have now added formulas too, it should

say Active. If it does not then the formulas have been inputted incorrectly.

Click on Speed and Acceleration for Reference Product Select Main Axis.

For Point Selection in Speed and Acceleration choose Point.1 in the part NewHook.

Click Simulation with Laws

Select Activate Sensors checkbox

Activate

Speed-Acceleration.1\X_Point1

Speed-Acceleration.1\Z_Point1

Speed-Acceleration.1\Y_Point1

Speed-Acceleration.2\Linear Acceleration

These will be what your simulation is measuring.

This is a representation of the movement of the point through time. In this scenario it is

simply a measure of the location of the point as it travels during the simulation. There are many

different options that you are capable of measuring and if your simulation is running according

to the math that you have tested you can find many other complex values through the

kinematics simulation instead of having to do math on every process.

Summary: Through this tutorial you have been given a basic understanding of the

kinematics simulation process. We touched on constraints and how they influence the

creation of joints. We demonstrated how to use joints to create the degrees of freedom

that we are looking for and remove the degrees of freedom that are not intended. We

went over how simulation with laws works and how to apply it with real mathematical

equations but it can be done with approximations or “random” numbers to give a

simulation.