Determine “how fast” parts of a machine are moving. Important when concerned with the timing of a mechanism. First step in acceleration analysis. Velocity Analysis Section 4

Velocity Linear –Straight line, instantaneous speed of a point. v A = 30 in/s 30 0 Rotational –Instantaneous speed of the rotation of a link.  2 = 72 rad/s, ccw 2

Linear and Angular Velocity For points on the same link v = r  Points have linear velocity (v) Links have rotational velocity (  ) B vAvA vBvB A 22 2 rBrB rArA

Relative Velocity Two points on a rigid body can only have a relative velocity: Perpendicular to the line that connects them. A B A B The motion of B relative to A (v B/A )

Relative Velocity Method Relative velocity equation is used to form vector polygons, and determine velocities of key points. v i = v j +> v i/j vivi v i/j vjvj

Problem 4-1 Determine the velocity of the piston, as the crank rotates at 600 rpm, cw. 2 in 8 in 65 0

Problem 4-7 Determine the rotational velocity of the crushing ram, as the crank rotates clockwise at 60 rpm. 60 mm 400 mm 180 mm 360 mm

Point on a Floating Link Must use simultaneous velocity equations v x = v i +> v x/i v x = v j +> v x/j X i j v X/i vivi vjvj v j/i v X/j vXvX Use the Velocity Image

Determines the amount that parts of a machine are “speeding-up” or “slowing down”. Important because a force is required to produce accelerations. Acceleration Analysis

Acceleration of a point, a, is caused by a change in velocity. Velocity can change its: Magnitude  tangential acceleration In direction of velocity if part is accelerating. Opposite direction of velocity if part is decelerating. Acceleration of a Point

Velocity can also change its: Direction  normal acceleration directed towards center of rotation (or relative rotation). Acceleration of a Point

Angular Acceleration Angular acceleration of a link,  is influenced by the tangential acceleration. B atBatB vBvB A 22 2 22 anBanB

Relative Acceleration Two points on a rigid body can only have a relative tangential acceleration: Therefore, the relative normal acceleration is: Perpendicular to the line that connects them. Parallel to the line that connects them.

Relative Acceleration Method Relative acceleration equation is used to form vector polygons, and determine the acceleration of key points. a i = a j +> a i/j Breaking each component into normal and tangential components gives: a i n +> a i t = a j n +> a j t +> a i/j n +> a i/j t

Acceleration Analysis Reminders Points on translating links have no normal acceleration. Points on links that rotate at constant speed have no tangential acceleration.

Problem 4-31 Determine the acceleration of the piston, as the crank rotates clockwise, at a constant rate of 600 rpm. 2 in 8 in 65 0

Problem 4-37 Determine the angular acceleration of the crushing ram, as the crank rotates clockwise at a constant rate of 60 rpm. 60 mm 400 mm 180 mm 360 mm

Point on a Floating Link Must use simultaneous acceleration equations a x = a i n +> a i t +> a x/i n +> a x/i t a x = a j n +> a j t +> a x/j n +> a x/j t i j X vivi vjvj vXvX v X/i v j/i v X/j a n X/j atjatj aXaX atiati aniani a t X/j a n X/i a t X/i a n j/i a t j/i

Problem 4-72 For the windshield wiper linkage shown, determine the acceleration of the cg of the connecting link. The motor is running at 30 rpm clockwise. 14 in 2 in 13 in 3.5 in in 6.7 in

Acceleration Image Must use total acceleration atjatj aXaX a n X/j atiati aniani a t X/j a n X/i a t X/i a n j/i a t j/i aiai a X/j a j/i a X/i