Types of Motion Translation a straight line keeps

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Types of Motion • Translation ( a straight line keeps its direction) 1. rectilinear

Types of Motion • Translation ( a straight line keeps its direction) 1. rectilinear translation 2. curvilinear translation • Rotation about a fixed axis ( particles remain in the same plane) • General Plane Motion • Motion about a fixed point • General Motion Kinematics - Plane motion ( particles remain in the same plane) Jacob Y. Kazakia © 2005 1

Translation r B = r A + r B/A y A r B/A has

Translation r B = r A + r B/A y A r B/A has constant direction during translation & r B/A has constant length since we have a rigid body B r. A r. B x z rectilinear translation: Kinematics - Plane motion consequently: v A = v B & a A = a B curvilinear translation: Jacob Y. Kazakia © 2005 2

Rotation about a fixed axis z f r r = r sin f 1

Rotation about a fixed axis z f r r = r sin f 1 rev = 2 p rad = 360 o the velocity vector v must be tangent to the circle r x O q(t) y tangential cmp. Kinematics - Plane motion Jacob Y. Kazakia © 2005 normal cmp. 3

Example 1 A y B 200 mm 0 12 300 mm z x D

Example 1 A y B 200 mm 0 12 300 mm z x D m m The bent rod ABCD rotates about AD with speed v = 95 rad/s ( velocity of C downwards). Determine the velocity and acceleration of point B. C D(0. 3, 0, 0) and A(0, 0. 2, 0. 12) hence Consequently: And we can now calculate the velocity and acceleration vectors for point B. Kinematics - Plane motion Jacob Y. Kazakia © 2005 4

Example 1 cont. A y B 200 mm 0 12 300 mm z x

Example 1 cont. A y B 200 mm 0 12 300 mm z x D Kinematics - Plane motion m m C Jacob Y. Kazakia © 2005 5

General Plane Motion v. A A v. B B y’ v. A B B

General Plane Motion v. A A v. B B y’ v. A B B Translation with A x’ A r. B/A v. B/A Rotation about A The angular velocity v of a rigid body in plane motion is independent of the reference point Kinematics - Plane motion Jacob Y. Kazakia © 2005 6

Example 1 40 o q A End A of the rod moves with speed

Example 1 40 o q A End A of the rod moves with speed v. A= 25 in/s to the right. Angle q = 250. Determine: 1. The angular velocity of the rod 2. The velocity of end B B 30 in 25 o Method 1: v. B B v. B/A 40 o B v. A B A A 25 o v. A v. B 40 o v. A 25 o v. A 180 -(40+65)=75 o v. B/A A 25 o vk 65 o Kinematics - Plane motion Jacob Y. Kazakia © 2005 7

Example 1 cont. B 30 in A Method 2: 40 o q End A

Example 1 cont. B 30 in A Method 2: 40 o q End A of the rod moves with speed v. A= 25 in/s to the right. Angle q = 250. Determine: 1. The angular velocity of the rod 2. The velocity of end B y x From the relation: We obtain: Kinematics - Plane motion Jacob Y. Kazakia © 2005 8

Example 2 v B A v. D r A = 120 mm r B

Example 2 v B A v. D r A = 120 mm r B = 60 mm r C = 45 mm C B v v. C v. B v. E v. C clockwise Kinematics - Plane motion Jacob Y. Kazakia © 2005 9

Example 3 b 80 mm B A v. B/A a = 3 rad/s counterclockwise

Example 3 b 80 mm B A v. B/A a = 3 rad/s counterclockwise Determine: v C/B 160 mm C and v D/C D 180 mm Kinematics - Plane motion 60 mm Jacob Y. Kazakia © 2005 10