Can someone give me the intuition behind not using time as a parameter

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teddyayalew
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Can someone give me the intuition behind not using time as a parameter for a Cycloid.
 
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Sorry I mean to say why is using the angle by which the wheel has turned more preferable than using time as a parameter. I understand both can be used.
 


Sorry I mean to say why is using the angle by which the wheel has turned more preferable than using time as a parameter. I understand both can be used.