A Rocker – a Crank

We connect a Linear-Motion FB (a Clock FB) to rotate the Rocker with a constant angular velocity.

This Step helps to understand:

1.'Centripetal Acceleration and Force' that is a result of the circular motion of the Centre-of-Mass
2.'Superposition of Gravitational and Centripetal Force'
3.Why the 'Moment of the Centripetal Force' equals zero.
STEP 1: Delete the Spring Force FB
or
Edit the Spring-Force FB and make the Spring-Rate = 0 N/mm
STEP 2: Add a Linear-Motion FB
STEP 3: Connect a wire from the output-connector of the Linear-Motion FB to the input-connector of the Motion-Dimension FB.

The Machine Speed Setting is 60RPM, or 1Cycle/second. 1Cycle/second = 2π radians/second.

The mechanism below shows the forces that act at the Pin-Joint.

Rocker-Forces-10

Addition of Vertical Forces acting on the Rocker (Point 2) : (↑+ve).

∑FV=0 : R2V(N) - 1(kg)*9.807(m/s/s) = 0;  R2V = 9.807N (upwards)

Addition of Horizontal Forces acting on the Rocker (Point 2) : (→ +ve).

∑FV=0 : +R2H(N) + 1(kg)*0.1(m)*(2π)2(1/s/s) = 0;  R2H = -3.948N (to the left)

Moments are:

•An Anti-clockwise Moment that acts on the Rocker is 0.98Nm - as before.
•The Centripetal Force acts through the centre of rotation. It does not apply a moment to the Arm. Hence, the Moment is the same.

Rocker-Forces-11

The image to the left is the same as the image above.

I have added to the image the Horizontal and Vertical Force Vectors that ACT-ON the Rocker

The two components are:

1.Reaction to the Gravitational Force - it acts on the Rocker. Equal to 9.81N
2.Centripetal Force acts on the Rocker to the left. Equal to 3.948N

The forces are perpendicular(⊥) when the Rocker is horizontal. Hence, we can use Pythagoras, to give 10.571N

Ftotal = √(Fg2 + Fc2) (Total Force = SQRT(SQR(Gravitation Force) + SQR(Centripetal Force)) = SQRT((m.g)2 + (m.r.ω2)2)

Total Force = √((1*g)2 + (1*0.1*(2π)2)2) = √(9.812 + 3.9482) = 10.571N

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd