Step 13.1A: Stationary Rocker

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Step 13.1A: Stationary Rocker

Forces that ACT ON a Rocker.

To understand how we calculate and show the Forces Vectors, we will start with a basic kinematic-chain.

•The kinematic-chain is a Rocker.

•The Base-Value of the Motion-Dimension FB controls the angle of the Rocker.

•The Motion-Dimension FB does not have a wire connected to its input-connector.

•We add a Profile / Extrusion to the Rocker, The Extrusion has mass and inertia.

Add the Model

A Rocker with Center-of-Mass Symbol(1) with Forces Display ON

A Rocker with Center-of-Mass Symbol(1) with Forces Display ON

STEP 1: Add a Rocker

1.Mechanism-Editor: Edit the Base-Part

2.Part-Editor: Geometry toolbar > Add a Line, Add Dimension | Drag to add the Line, and add dimensions to locate the line and define its length.

3.Part-Editor : Constraints toolbar > Add Horizontal to make the Line horizontal. Close the Part-Editor

4.Mechanism-Editor : Mechanisms menu > Add Part | Drag to add the Part

5.Mechanism-Editor : Mechanisms menu > Add Pin-Joint | Click the start-Point of the Part, and the end-Point (the right-side Point of the horizontal Line) in the Base-Part.

6.Mechanism-Editor : Function-Blocks menu >  Motion-Dimension FB | Click the Pin-Joint, the Lines in the Base-Part and the Part, OK-tiny-11-15 the Command-Manager.

STEP 2: Add a sketch-loop, and a Profile/Extrusion.

1.Edit the Rocker Part

2.Part-Editor : Geometry toolbar > Add Lines / Add Arcs (40mm Radius) | to add a sketch-loop. Do the Hover+Drag technique to merge the end-Points of each sketch-element (see Tutorial 3)

3.Part-Editor: Geometry toolbar > Add Coincident Constraints | to move the center-Point of each Arc to the start-Point and end-Point of the CAD-Line along the Rocker

4.Part-Editor: Geometry-Editor | Edit the length of the CAD-Line to equal 200mm. Exit the Part-Editor.

5.Mechanism-Editor: Solids menu (or toolbar) > Add Profile | Click the sketch-loop, Click OK-tiny-13-17 in the Command-Manager.

6.Mechanism-Editor : SHIFT-CLICK the Profile

7.Selection-Window: In the Selection-Window, Right-click the Extrusion element, Click Edit element to open the Extrusion dialog.

8.Extrusion dialog >  Mass-Properties : Edit the Density = 4756kg/m3 with the Extrusion Depth =10mm to make the Mass of the Extrusion ~1kg*

9.Close the Extrusion dialog.

* From the shape of the Extrusion, we calculate for you its Mass(kg), its Mass Moment-of-Inertia(kg.m2), and its center-of-mass.

In this case, because the sketch-loop is symmetrical and equal to the length of the Part - the center-of-mass is 100mm from the Start-Point of the CAD-Line in the Part.

The symbol for the center-of-mass is the GST-PointSymbol - see image above Red-14-1b

Calculate and Display the Force Vectors

There are two icons in the Forces menutoolbar: Calculate and Display Force Vectors.

GST-Icon-Force-Calculate-ON

Mechanism-Editor: Click Force toolbar > Calculate Forces

GST-Icon-Force-Vectors-Show

Mechanism-Editor: Click Force toolbar > Display Force Vectors

When a minimum of one Part has mass, we calculate for you and we display Force Vectors.

The Force-Vectors give the direction, location, and magnitude of each Force.

Notes

Use the Force and Torque Vector Scale buttons to increase or decrease the length of the vectors if they are too long or too short to see easily.

Analyze the Forces

GST-13-1A01

Force Analysis - Information Provided:

•Action / Reaction Force-Vectors at each joint.

•Moment at the Pin-Joint, which is equivalent to the Load-Torque or Application-Torque that an idealized Power Source must provide to the Rocker.

•Motor symbol (in Purple) at the Pin-Joint. The Motor symbol identifies the location of the Power Source.

•The Part-Outline and the Force-Vectors that act on a Part are the same color.

•There are two Parts in the model - the Base-Part and the Rocker - therefore, there are two vector colors.

GST-13-1A02

Move your mouse-pointer to the Part-Outline of the Rocker.

The Force-Vectors that ACT ON the Rocker are now Red.

Vertical Forces (N) acting on the Rocker - Upwards is +ve

Moments (N.m) at the Pin-Joint - Counter-clockwise is +ve

Force explanation of the RED Force Vectors and Moments

Red-14-1b Gravitational Vector - not shown = 1kg*9.806kg/m/s/s = 9.806N

Red-14-2 Vertical Force - 9.806N acts upwards. The reaction force from the Base-Part that acts on the Rocker. The Rocker would fall freely downwards if the Base-Part did not react to support the Rocker with a vertical Force.

Red-14-3 Counter-Clockwise Moment = 0.98Nm. The reaction moment from the Base-Part that acts on the Rocker . The Rocker would rotate freely clockwise if the Base-Part did not react with this Torque to prevent the Rocker rotating.

GST-13-1A03

 

Now move your mouse-pointer to the vertical Force-Vector that acts on the Base-Part.

All vectors that ACT ON the Base-Part turn Red.

There is:

Red-14-1b Vertical Force 9.81N downwards, that acts on the Base-Part. This is the Gravitational Force that acts-on the Base-Part.

Red-14-2 Clockwise Moment (Torque) of 0.98Nm that acts on the Base-Part.

GST-13-1A04

Edit the Motion-Dimension FB to rotate the Rocker until it is vertical

•My mouse-pointer is above the Part-Outline of the Rocker - the Part-Outline and the Force-Vector become Red.

• Vertical Force = 9.807N.

This is the same vertical force as when the Rocker was horizontal. This is not a surprise. The Part has the same mass and it is the only joint through which the force can act.

•Torque Moment = 0Nm

The Center-of-Mass of the Rocker above the Pin-Joint. Therefore, the Rocker does not need a Torque to hold it in the vertical position.