Kinematics - Plane motion Jacob Y. Kazakia © 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

Kinematics - Plane motion Jacob Y. Kazakia © 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:

Kinematics - Plane motion Jacob Y. Kazakia © 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.

Kinematics - Plane motion Jacob Y. Kazakia © Example 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.

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

Kinematics - Plane motion Jacob Y. Kazakia © 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

Kinematics - Plane motion Jacob Y. Kazakia © Example 1 30 in    End A of the rod moves with speed v A = 25 in/s to the right. Angle  = 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      

Kinematics - Plane motion Jacob Y. Kazakia © Example 1 cont. 30 in    End A of the rod moves with speed v A = 25 in/s to the right. Angle  = 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:

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

Kinematics - Plane motion Jacob Y. Kazakia © 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