1. Kinematics - Plane motion Jacob Y. Kazakia © 20051 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 ( particles remain in the same plane) Motion about a fixed point General Motion

2. Kinematics - Plane motion Jacob Y. Kazakia © 20052 Translation rArA rBrB A B x z y r B = r A + r B/A r B/A has constant direction during translation & r B/A has constant length since we have a rigid body consequently: v A = v B & a A = a B rectilinear translation: curvilinear translation:

3. Kinematics - Plane motion Jacob Y. Kazakia © 20053 Rotation about a fixed axis  t    r y z x O  = r sin  1 rev = 2  rad = 360 o the velocity vector v must be tangent to the circle normal cmp. tangential cmp.

4. Kinematics - Plane motion Jacob Y. Kazakia © 20054 Example 1 300 mm 200 mm 120 mm A B C D x y z The bent rod ABCD rotates about AD with speed  = 95 rad/s ( velocity of C downwards). Determine the velocity and acceleration of point B. 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.

5. Kinematics - Plane motion Jacob Y. Kazakia © 20055 Example 1 cont. 300 mm 200 mm 120 mm A B C D x y z

6. Kinematics - Plane motion Jacob Y. Kazakia © 20056 General Plane Motion A B A BB A vAvA vAvA vAvA vBvB v B/A y’ x’ r B/A Translation with A Rotation about A The angular velocity  of a rigid body in plane motion is independent of the reference point

7. Kinematics - Plane motion Jacob Y. Kazakia © 20057 Example 1 30 in    End A of the rod moves with speed v A = 25 in/s to the right. Angle  = 25 0. Determine: 1.The angular velocity of the rod 2.The velocity of end B Method 1: A B A B A B A B   vAvA vBvB   vAvA vAvA v B/A  k k vAvA vBvB      

8. Kinematics - Plane motion Jacob Y. Kazakia © 20058 Example 1 cont. 30 in    End A of the rod moves with speed v A = 25 in/s to the right. Angle  = 25 0. Determine: 1.The angular velocity of the rod 2.The velocity of end B A B Method 2: x y From the relation: We obtain:

9. Kinematics - Plane motion Jacob Y. Kazakia © 20059 Example 2 BB CC    C vDvD vBvB vEvE vCvC r A = 120 mm r B = 60 mm r C = 45 mm clockwise

10. Kinematics - Plane motion Jacob Y. Kazakia © 200510 Example 3 80 mm 160 mm 180 mm60 mm a   B/A = 3 rad/s counterclockwise Determine:  C/B and  D/C A B CD