Step 13.1A: A Stationary Rocker

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Step 13.1A: A Stationary Rocker

Forces that ACT ON a Rocker.

To understand how MechDesigner calculates and shows Forces Vectors, we will start with a very basic kinematic-chain.

The kinematic-chain is a:

Rocker

To begin, the Rocker does not move.

To model the Rocker we do not need to connect a wire connected to the input-connector of its Motion-Dimension FB.

The Motion-Dimension specifies the Base-Value of the Rocker.

Rocker-Forces-1

The kinematic-chain, to the left, is kinematically-defined ( Green Part-Outlines).

A Rocker is horizontal and 200mm long.

The Rocker has mass.

The mass is calculated by MechDesigner from the Extrusion Density, Extrusion Depth (see: Extrusion dialog-box) and the shape of the Profile.

The shape of the Profile is a sketch-loop (see Pink Profile, sketch-loop).  

 

Add the Profile and specify its shape:

a.Edit the Rocker Part

b.Part-Editor : Geometry toolbar > Add Lines and Add Arcs | Do the Hover+Drag technique to merge the end-Points of each sketch-element.

c.The length of the oval is equal to the length of the Part. Exit the Part-Editor.

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

e.Edit the Extrusion element to open the Extrusion dialog-box.

f.Edit its Density, or the Extrusion Depth, to make the Mass = 1kg .

In addition to its Mass(kg), MechDesigner finds its Moment-of-Inertia(kg.m2) and the position of the center-of-Mass relative to the Origin of the CAD-Line.

In this case, because the oval shape is symmetrical and equal to the length of the Part, the center-of-mass is 100mm from the Pin-Joint; the mid-point along the Part.

MechDesigner identifies the center-of-mass of the Part with a small 'position' symbolRed-14-1b.

Icon-Force-Calculate-ON

Force toolbar > Calculate Forces to Calculate Forces

Icon-Force-Vectors-Show

Force toolbar > Display Force Vectors to Show Force Vectors

If a minimum of one Added Part has a mass, MechDesigner shows Force Vectors. The Force-Vectors give the direction and magnitude of each Force. (Note if the Force Vectors do not show, click the 'Rebuild' tool, and also you may need to Run toolbar > Cycle  (ALT+C key combination) to run the model.


If necessary, increase or decrease the length of the Force and Torque Vectors with the Force Vector Scale and Torque Vector Scale buttons.

If necessary, change the background color of the graphic-area to Grey , or a dark color, so that it is easier to see the textual force magnitude, at the end of each Force-Vector.


Rocker-Forces-2

The Force Analysis calculates Kinetostatic Force and Moments - these are those Forces that an Idealized Power Source must provide to imposed the motion-design on the kinematic-chains.

The force analysis shows the action and reaction of the kinetostatic-force vectors at each joint.

In this force analysis, there are two Points at the Pin-Joint :they are Point 1 on the Base-Part, Point 2 on the Rocker.

The force analysis shows the Torque at the Pin-Joint. The Torque is the Power Source that must hold the Rocker in place.

There is a Motor symbol (in black) at the Pin-Joint. The Motor symbol identifies the location of the Power Source.

Each Part-Outline changes its color. The Part-Outline and the Force-Vector that acts on that Part become the same color.

Force Vectors that act on the Rocker

Move your mouse-pointer to the Part-Outline of the Rocker Part. You will see that the Force-Vectors that ACT ON the Rocker become Red.

The summation of the Vertical Forces acting on the Rocker (Point 2) : (upwards is +ve).

∑FV=0 : R2(N) - 1(kg)*9.807(m/s/s) = 0; R2 = 9.807N (upwards)

Take Moments about Point 1, acting on the Rocker, Point 2:  (Counter-clockwise is +ve)

∑M1=0 ; M1 - 0.020(m)*1(kg)*9.81(m/s/s) = 0 ; M1 = 0.9807Nm

Red-14-1b Gravitational Vector - not shown. There is, however, a vertical gravitational force of (1(kg)*9.807(kg/m/s/s))=9.81N

Red-14-2 Vertical Force of 9.81N  acts upwards. The Base-Part's reaction force acts on the Rocker. The Rocker would fall freely if the Base-Part did not resist Rocker with the vertical Force.

Red-14-3 Counter-Clockwise Moment (Torque) of 0.98Nm.. The Rocker would rotate freely clockwise if the Base-Part did not resist the Rocker with this Torque.

Rocker-Forces-4

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.

Rocker-Forces-5

Now, the same Rocker is vertical. (To do this, edit the Base-Value in the Motion-Dimension FB to +90º, or 270º).

My mouse-pointer is above the Part-Outline of the Rocker, so that the Part-Outline and the Force-Vector are Red.

You can see that the Vertical Force, 9.807N, is the same as before. This is not a surprise. The Part has the same mass and it is the only joint through which the force can act.

The Moment is now 0Nm. This is because the center-of-Mass of the Rocker is vertically above the Pin-Joint. The Rocker 'balances' directly above the Pin-Joint, and hence, a Torque is not necessary to hold the Rocker.

Edit the Motion-Dimension FB again to make the Base-Value 0º, or 180º)