﻿ Step 13.1A: A Stationary Rocker

# Step 13.1A: A Stationary Rocker

### Forces that 'Act On' a Rocker.

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

The kinematic-chain is a:

 • Rocker

The Rocker does not move. The Rocker does not have a wire connected to the input-connector of Motion-Dimension FB.

The kinematic-chain to the left is a kinematically-defined chain [ Green Part Outlines].

It is a Rocker that is horizontal and 200mm long.

The Rocker has a 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 specified by the sketch-loop [see Pink

To add the Profile and specify its shape:

 a. Use the Part-Editor to add an 'oval' sketch-loop to the Rocker Part. Make the length of the oval equal to the length of the Part, then exit the Part-Editor.
 b. Use Solids menu (or toolbar) > Add Profile: Click the sketch-loop, then OK in the Command-Manager.
 c. Edit the Extrusion element to open the Extrusion dialog-box.
 d. 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.m^2] and the position of the Centre-of-Mass .

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

MechDesigner identifies the centre-of-mass of the Part with a small 'position' symbol.

Calculate Forces

Click Forces Toolbar > Calculate Forces so that the icon becomes the same as the icon to the left.

Display Force-Vectors

Click the Forces Toolbar > Display Force Vectors so that the icon becomes the same as the icon to the left.

'Force': when we use the word 'force', it will refer to a 'generalised force', which will include 'moments'.

If a minimum of one Part has a mass, MechDesigner shows the 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]

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

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

 • 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 - Point 1 on the Base-Part and 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 at the Pin-Joint. The Motor symbol identifies the location of the Power Source.
 • Each Part-Outline changes its colour. The Part-Outline and the Force-Vector that acts on that Part become the same colour.

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

Gravitational Vector - not shown. There is, however, a vertical gravitational force of [1[kg]*9.807[kg/m/s/s]]=9.81N

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.

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.

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:

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

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

Now, the same Rocker is vertical. [To do this, edit the Base-Value in the Motion-Dimension FB to +90º].

My mouse-pointer is above the Part-Outline of the Rocker, so that the Part-Outline and the Force-Vector have become 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 Centre-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.

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