A Rocker and a Spring

In this topic, we balance the forces that act on the Rocker with a Spring.

The Downward Force and Clockwise Moment on the Rocker that result from Gravitational Force

...will be balanced by...

An Upward Force and Counter-Clockwise Moment on the Rocker from a Spring

The Rocker is stationary.

MD-QST13-2-1

A Spring FB exerts a force between two Points in two different Parts. In this case, a Point in the Rocker and a Point in the Base-Part.

STEP 1: Edit the Base-Part to add a Line

Add the Line so that one of its Points1s-red is 100mm below the end of the Rocker Part, when the Rocker is horizontal.

Step 1 is complete.

TOP-TIP: Use Tools menu > Show/Hide other Mechanisms to make the Rocker visible (in Grey) when you edit Parts in the Part-Editor.

 

STEP 2: Close the Part-Editor

Icon-FB-ForceSpring

STEP 3: Click Force Toolbar > Add Spring-Force FB

To add the Spring Fb, you must click a Point in two different Parts

Rocker-Forces-6

STEP 4: Click two Points1s-red2s – as indicated to the left.

Click the point that is the end-Point of the CAD-Line in the Rocker and not the centre-Point of the Arc[+].

Click the end-Point of the Line in the Base-Part that is 100mm below the Rocker

The order you select the Points is not important.

The Points become the Anchor-Points for the Spring Fb.

Dialog-FB-SpringForce-SprPara

Steps 5,6,7 may not be necessary, as the Spring-Force FB should be enabled automatically.


If necessary, we must enable the Spring FB

We must use the Spring-Force FB dialog-box.

STEP 5: Double-click the Spring FB in the graphic-area to open the Spring FB dialog-box

If necessary, click the Spring Parameters separator to see its parameters.

STEP 6: Click the Enable Spring FB check box

The tick should show in the check-box.

Do not edit the Spring or Velocity Factors.

STEP 7: Click OK-tiny-13-17

Rocker-Forces-7

The image to the left shows the Spring Function-Block1s-red and the Symbol2s that represents the Spring.

The Spring FB does not exert a Force, yet. Thus, MechDesigner does not show Forces at the Spring's anchor-points.

STEP 5: Double-click the Spring FB in the graphic-area to open the Spring FB dialog-box, again

'Constant Force'

MD-QST13-2-6

We can balance the Gravitational Force if we edit the Constant Force parameter in the Spring Force dialog-box.

A positive 'Constant-Force' pulls the Spring's anchor-points together. A negative 'Contact-Force' pushes the Spring's anchor-points apart.

STEP 9: Enter a Constant Force = -9.80665N in the Spring FB dialog-box to exert 9.80665N upwards against the Rocker Part.

Rocker-Forces-8

Addition of Vertical Forces acting on the Rocker [Point 2] : [upwards +ve].

∑FV=0 : R2[N] -1[kg]*9.807[m/s/s] + 9.807[N] = 0; R2 = 0N

Addition of Horizontal Forces acting on the Rocker [Point 2] : [upwards +ve].

∑FH=0 : R2H[N] = 0;  R2H = 0N

Take Moments about 1, acting on the Rocker [Point 2]:  [Counter-clockwise +ve]

∑M1=0 ; M2 + 0.2[m]*9.81[N] - 0.1[m]*9.81[N] = 0 . Thus M2= -0.981Nm.

 

Rocker-Forces-9

Spring-Rate and Free-Length

You can use the Spring-Rate and Free-Length Parameters to obtain the same result. We will enter a 'Free-Length' and 'Spring-Rate' so that the Spring exerts a force equal and opposite to the Gravitational Force. Also, edit the Constant Force = 0N again.

MD-QST13-2-8

When we make the Free-Length = 110mm and the Spring-Rate = 0.980665N/mm, the Spring FB will exert 9.80665N upwards.

Why?

The model defines the actual distance between the Spring FB's two anchor-points = 100mm. Thus, the Spring FB is deflected by 10mm

Therefore, the Spring FB exerts a Force = 10mm * 0.98066N/mm =  9.81N upwards on the Rocker.

Note:

The Spring Force FB has:

Two output-connectors.

From the top output-connector:

Distance, linear velocity and linear acceleration between the two Points

From the bottom output-connector

Total Force, X-Force and Y-Force. The X and Y-Force components are relative to the coordinate axes of the Mechanism-Plane.

One input Connector: A Force Function can be added to the input from a Maths FB.

Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd