Relative-Motion Analysis: Velocity

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Relative-Motion Analysis: Velocity. y. Translation only Kinematics Position Velocity Acceleration. r A. r B. x. A. B. Relative-Motion Analysis: Velocity. d r A. d θ. y. Transl. & Rotation (General Plane Motion) Position Velocity (time deriv ) where - PowerPoint PPT Presentation

Transcript of Relative-Motion Analysis: Velocity

Rigid-Body Mechanics

Relative-Motion Analysis: VelocityTranslation onlyKinematicsPosition

Velocity

Acceleration

AB

xyrArB

Relative-Motion Analysis: VelocityTransl. & Rotation(General Plane Motion)Position

Velocity (time deriv)

where

and ( is rotation of member about A)AB

xyrArBddrAdrBdrArB/ArB/A (new)drB/A

For our problems, we will just need to plug in for each of these variables to get vB.and often

Review of Cross ProductsSee Section 4.2 for full details

orTo use, must define right-hand x, y, z coordinate systemExample ProblemIf rod AB slides along the horizontal slot with a velocity of 60 ft/s, determine the angular velocity of link BC at the instant shown. (F16-11, 48 rad/s)

What about the velocity of the pin at C, and the angular velocity of wheel OC at that instant?(104 ft/s up)Special Case for Velocity SolutionRolling without slip

Can also have slip, in that instance direction of vA is at least known but magnitude unknownExample ProblemA bowling ball is cast on the alley with a backspin of = 10 rad/s while its center O has a forward velocity of vO = 8 m/s. Determine the velocity of the contact point A in contact with the alley. (16-58, 9.20 m/s to the right)

Instantaneous Center of Zero VelocityRolling without slip (not always)

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?

What if we want velocity at each point on rim?(each point will instantaneously rotate about axis fixed to that point)

Instantaneous Center of Zero VelocityDoes an I.C. always exist?At some instant, yesConsider 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 pointDraw perpendicular lines from eachIntersection is I.C. at that instantTo solvevPoint = rPoint/IC

Graphic Examples

To find I.C.Identify instantaneous directionof velocity for each pointDraw perpendicular lines from eachIntersection is I.C. at that instantTo solvevPoint = rPoint/ICExample ProblemIf 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)