Using Mathematica – An Example

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A Mountain Bike Suspension (Problem 5.25)

At the point of Crossing a Bump’

2 is at 221 2 is 205 rad/sec CW

2 is at 60 rad/s2 CW

Design Starts: Links to Vectors

r1

r2

r3r4

1 2 4 3r r r r

Basic Loop Equation:

Knowns and Unknowns:

• Knowns:– Magnitudes of all the vectors 1 = 180 - 61 = 119 and 2 = 221

– Velocity and Acceleration of these two angles (1 is fixed!)

• Unknowns: 3 and 4

– We seek angular velocity and acceleration of Link 3

Writing Loop Equation in Component Form:

• We must develop a model for our unknowns – following the text example

• Isolate 4 in both, Square and isolate 3

• Considering the ½ solutions to build a model for tan(½3)

• Take 1st Derivatives of component eqns build velocity models

• Take 2nd Derivatives of Component eqns to get Accel models

• Isolate the 3 terms!

The “Key”: Velocity

Accel: