Using Mathematica – An Example Live on your Computer!

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Presentation transcript:

Using Mathematica – An Example Live on your Computer!

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/s 2 CW

Design Starts: Links to Vectors r1r1 r2r2 r3r3 r4r4 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(½  3 ) Take 1 st Derivatives of component eqns build velocity models Take 2 nd Derivatives of Component eqns to get Accel models Isolate the  3 terms!

The “Key”: Velocity

Accel: