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Unformatted text preview: 1 Week 5 Week 5 (1) Velocity analysisanalytical method (review) (2) Acceleration analysis  analytical method (Unit Vector Method ) (ch7, Norton; ch8, M &R) Week 5 Fixed and moving reference frame Applied to mechanisms, we have a fixed reference frame, and a moving reference frame that is attached to one of the links R P = R O + R V P = V o + V + ω × R XYZ : fixed coordinate xys: moving coordinate 2 Week 5 The velocity equation V P = V o + V + ω × R … Equation 8.16 (M&R) V P = velocity of point P in the XYZsystem V O = velocity of origin of xyzsystem relative to XYZ system V = velocity of point P relative to xyzsystem ω = angular velocity of xyzsystem relative to XYZ system R = distance from origin of xyzsystem to point P Week 5 Locating the Moving Axis There are 3 classes of mechanisms to consider: 1. 4 bar pin jointed mechanisms 2. Sliding motion transfer 3. Rolling motion transfer 3 Week 5 Moving Axis  4 bar, pin jointed Place the origin on the pin connecting the driving link to the intermediate or motion transfer link (normally designated as link 3) Align the xy axis system with link 3 {outcome: V is zero} Week 5 Moving Axis  4 bar, pin jointed Y X x y P V P = Vo + ω × R O ω × R = ω k × R i =  ω R j 4 Week 5 Moving Axis  sliding connection outcome: R is zero, path of V is known (along the x axis) y x X Y P V P = Vo + V V = V i Week 5 Moving Axis  rolling connection outcome: R is zero, path of V is known NB xy axis moves with cam. “P” is on link 4, and appears to move along the y axis....
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 Three '09
 WeihuaLi
 Velocity, Unit Vector method

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