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I Velocities when generating an Archimedean spiral trajectory

  1. Aug 6, 2017 #1
    hey, I just want to know, if I am to send a velocity commands to generate a spiral trajectory, What would be these velocities (angular and linear)??
    Thanks in advance
     
  2. jcsd
  3. Aug 6, 2017 #2

    Charles Link

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  4. Aug 6, 2017 #3
  5. Aug 6, 2017 #4
    Since the usual definition of the Archimedes Spiral takes the angle as the input, it means you choose the angular velocity ω. Regarding linear velocity, I don't have an exact formula at hand, but since it gets closer to a circle with increasing angle, the linear velocity will asymptomatically approach ωr.
     
  6. Aug 6, 2017 #5

    Charles Link

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    For the OP @Benyoucef Rayane A google shows the Archimedes spiral has ## r=\theta^a ## with ## a=1 ##. This means ## r=\theta ## for this spiral. We can write the velocity ## \vec{v}=(\frac{dr}{dt}) \hat{a}_r+(r \dot{\theta}) \hat{a}_{\theta} ##. We have for ## r=\theta ##, that ## \frac{dr}{dt}=\dot{\theta}=\omega ##. This gives ## \vec{v}=\omega \hat{a}_r+(r \omega) \hat{a}_{\theta} ##. As ## r ## gets large, ## \vec{v} \approx (r \omega ) \hat{a}_{\theta} ## as @rumborak pointed out.
     
  7. Aug 12, 2017 #6

    Thanks guys, I got it now.
     
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