l16anno - Plane Motion of a Rigid Body Points P and Q are...

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Plane Motion of a Rigid Body Points P and Q are fixed on the rigid body B that is in plane motion relative to the x-y plane that is fixed in the reference frame T
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Rigid body: distance between any two points is constant Plane Motion: All points move parallel to the x-y plane All points P ’ located at r OP + z k are identified by point P, etc . x z ' P P y ,' P P x y OP r OP r
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cos sin ) ) si ) ( (n ( OQ OP PQ QP P Q P P Q Q r r r θθ θ = + =+ + + + = = = × × = rr r r vv r ri j j ki j k v r k vr ω ω ±± ± ± ± ± ± ± ± Velocity Angular Velocity ω
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θ = ω k ± Angular velocity of B. Angular velocity is independent of the points P and Q; it is a property of the motion of B P S R Q ' 0 ' QP P P Q SR R R S θφ θθ φ =+ =+=+ ×= + × × × = vv k r v r k r v ω ω r ± ± ±± ± ± ± constant φ= ω S , RP Q
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2 is the angular accel () ( ) (( c o s s i n ) ) s i n c o s ) ) (c o s s eration QP P Q P P Q PP Q P PQ P Q Q Q r r r θθ θ × =+ × = ×= ×× = × + + −+ =− = × × + aa α r vv ω r vk r k r k r ωω rk k r kk i j ki r ω j i k r α r ± ±± ± ± ± ± ± ± 2 2 in )) Q Q P Q × k r r j r ± ± Acceleration
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() QP P Q Q P PQ =+ × × + ×× vv ω r aa α r ωω r “ The Formula”
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“Recipe”
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This note was uploaded on 01/26/2012 for the course TAM 212 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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l16anno - Plane Motion of a Rigid Body Points P and Q are...

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