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V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
June 16, 2019
Question

Bike and Catenary

  • June 16, 2019
  • 1 reply
  • 3508 views

Can you show it with Mathcad - the bikeway is parts of catenary!

Catenary-Bike.png

1 reply

W
Werner_E25-Diamond I
25-Diamond I
June 16, 2019
@ValeryOchkov wrote:

Can you show it with Mathcad - the bikeway is parts of catenary!

Its more fun to create a wooden model

B.png

(see: https://www.macfunktion.ch/mathe/erstaunlich/quadrad/index.shtml)

or https://www.youtube.com/watch?v=QHLFJ2YoKGg

or https://www.youtube.com/watch?v=LgbWu8zJubo

 

But the ride would be very jerky in horizontal direction if the wheels are turned with constant angular velocity, even though some authors are talking about a "smooth" ride.

 

W
Werner_E25-Diamond I
25-Diamond I
June 16, 2019

OK, making a Mathcad animation is fun, too, and as you can see, the horizontal movement is indeed quite jerky.

Square_Wheel1.gif

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    June 17, 2019

    Thanks Werner!

    Today I woke up early and went out onto the veranda of my country house. The morning is beautiful, the sun is shining, the flowers are blooming in the garden and fragrant, birds are singing with might and main. I have ambitious plans for this day - to work even with the most interesting STEM-article on the Mathcad and the kinematics of a bicycle. On top of that, I open the Internet and see there an excellent solution to the problem by Werner. There are wonderful moments in life.

    For complete happiness, I would like to see the Mathcad 15 sheet!

    And What about a bicycle with three-cornered wheels, two-angled wheels (a straight line segment with a hole in the middle), and wheels with the shape of any convex polygon. After all, the wheel is a regular convex polygon with an infinite number of corners!

    PS

    Ten kilometers from my country house is the place where the great mechanical scientist Tchebyshev was born. Today I will sit on my bike and once again visit this place of pilgrimage for mathematicians.

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