Содержание
- 2. In particular, you will Determine why S-curves are necessary Review the ideal S-curve. Consider constant acceleration
- 3. Why S-curves? Reviewing the trapezoidal trajectory profile in speed v, we examine points 1, 2, 3,
- 4. Ideal S-curve t t = T vo vs v 1 as ar 1 Concave Convex t
- 5. Ideal S-curve equations The form assumed for the S-curve velocity profile is v(t) = co +
- 6. Concave period The concave conditions are v(0) = vo a(0) = 0 a(T/2) = as j(0)
- 7. Concave period Applying the initial and final conditions, we get the equations for s (position), v,
- 8. Ideal S-curve observations If we let Δv = vs - vo and define ar = Δv/T
- 9. Convex period This period applies for T/2 ≤ t ≤ T. Letting time be zero measured
- 10. Convex period Applying the initial and final conditions, we get the equations for s (position), v,
- 11. Distance traversed Adding in the distance at the halfway point gives the total distance traversed in
- 12. Max jerk transitions An ideal S-curve cannot transition smoothly between any speed change using a specified
- 13. Max jerk transitions Given a jerk jm, a starting speed vo, and the ending speed vs,
- 14. Speed transitions If v1 > v2 (overlap), we can determine an intermediate transition point using speed
- 15. Speed transitions
- 16. Speed transitions The pertinent equations are: vo + ao Tt + jm Tt 2/2 = vs-
- 17. S-curve with linear period If v1
- 18. S-curve with linear period Motion conditions: Phase 1 - Concave Phase 2 – Linear Phase 3
- 19. S-curve with linear period Phase 1 – Concave motion conditions: s(t) = vo t + jm
- 20. S-curve with linear period Phase 2 – Linear motion conditions: s(t) = v1 t + as
- 21. S-curve with linear period Phase 3 – Convex motion conditions: s(t) = v2 t + as
- 22. S-curve context How is the S-curve applied in the real world? Robots and machine tools are
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