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ESPN Sports Science Blake Griffin

ESPN Sports Science Blake Griffin. Relative-Motion Analysis: Velocity. d r A. d θ. y. Transl. & Rotation (General Plane Motion) Position Velocity (time deriv ) where and ( ω is rotation of member about A). r B /A. r B /A (new). d r A. d r B /A. d r B. r A. r B. x. A. B.

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ESPN Sports Science Blake Griffin

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  1. ESPN Sports Science Blake Griffin

  2. Relative-Motion Analysis: Velocity drA dθ y • Transl. & Rotation (General Plane Motion) • Position • Velocity (time deriv) where and (ω is rotation of member about A) rB/A rB/A (new) drA drB/A drB rA rB x A B For our problems, we will just need to plug in for each of these variables to get vB.and often ω

  3. Instantaneous Center of Zero Velocity • Relate velocity of two points on right body • What if choose a point A which is instantaneously stationary (i.e. vA = 0) • Can we find an instant point with this property to relate to? Rolling without slip (not always) What if we want velocity at each point on rim? (each point will instantaneously rotate about axis fixed to that point)

  4. Instantaneous Center of Zero Velocity • Does an I.C. always exist? • At some instant, yes • Consider curvilinear motion in particle mech. • For rigid body? • I.C. need not be ON the body? • To find I.C. • Identify instantaneous directionof velocity for each point • Draw perpendicular lines from each • Intersection is I.C. at that instant • To solve vPoint = ωrPoint/IC

  5. Graphic Examples • To find I.C. • Identify instantaneous directionof velocity for each point • Draw perpendicular lines from each • Intersection is I.C. at that instant • To solve vPoint = ωrPoint/IC

  6. Example Problem If link CD has an angular velocity of 6 rad/s, determine the velocity of point E on link BC and the angular velocity of link AB at the instant shown. (16-89, 6 rad/s CCW, 4.76 m/s, 40.9° above – x)

  7. Relative-Motion Analysis: Acceleration drA dθ y • Transl. & Rotation (General Plane Motion) • Position • Velocity (dr/dt) • Acceleration (dv/dt) rB/A rB/A (new) drA drB/A drB rA rB x A Rotation about A B Magnitude of Components:

  8. Relative-Motion Analysis: Acceleration How do we relate motion of these?

  9. Example Problem The hydraulic cylinder extends with a velocity of 1.5 m/s and an acceleration of 0.5 m/s2. Determine the angular acceleration of link ABC and the acceleration of end C at the instant shown. Point B is pin connected to the slider block. (16-122, 41.6 rad/s2, 38.2 m/s2, 39.4° below x)

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