Planar Kinematics of a Rigid Body: Review II 1. Relative motion 2. Strategy for solving kinematics problems ME 316 Handout 2

Relative Motion 1. Absolute Motion When the motion of an object is viewed by taking the earth as the reference body, the motion of the object is called the absolute motion. ME 316 Handout 2

Relative Motion “Absolute motion” A reference object An object The earth An object A reference object “Absolute motion” ME 316 Handout 2

Relative Motion 2. Relative Motion The reference object is another object, say B. The motion of A is viewed with reference to B. B: reference body A/B ME 316 Handout 2

Relative Motion The relative motion of objects A and B can also be a general planar motion (i.e., the translation plus a rotation around a point on the object). ME 316 Handout 2

Relative Motion 3. Relative motion equation ME 316 Handout 2

Relative Motion Relative rotation (B: reference body) Absolute angular velocity of body B Relative angular velocity Absolute angular velocity of body A ME 316 Handout 2

Relative Motion the angular velocity of the assembly of A and B. the relative angular velocity of object A with respect to object B ME 316 Handout 2

Relative Motion Relative translation (B: reference body) Relative Translation is measured by two points selected from body A and body B, respectively ME 316 Handout 2

Relative Motion PB PA Relative translation (B: reference body) - Suppose the translating axis is - Pick up two points PA and PB on body A and body B - Project the velocities at PA and PB along ME 316 Handout 2

Relative Motion Relative translation between any two points on different bodies (the previous figure on page 9) Absolute velocity of point PB Relative velocity Absolute velocity of point PA ME 316 Handout 2

(Total) Relative Motion (Velocity) Relative Translation Relative Rotation (Total) Relative Motion (Velocity) ME 316 Handout 2

Relative Motion When two objects are joined into a relative translation relation and their angular velocity is zero, we have ME 316 Handout 2

Relative Motion When two objects are in contact, at their contact point (PA and PB), the relative translation between these two points are: A B A B PA PB ME 316 Handout 2

Relative Motion: Example ME 316 Handout 2

Relative Motion Question (a). What is the relative angular velocity between gear B and arm AB, in particular taking arm AB as a reference object? Question (b). What is the angular velocity of gear A if we have found that the relative angular velocity of gear A with respect to gear B is 0.5 rad/sec clockwise? ME 316 Handout 2

Relative Motion Solution (to be filled) ME 316 Handout 2

Relative Motion Solution (to be filled) ME 316 Handout 2

Solving Kinematics Problem Transfer: Known variables -> Unknown variables Begin with a single body and then a system of bodies Translation Rotation at a fixed axis General plane motion Motion transfer ME 316 Handout 2

Solving Kinematics Problem Case 1. A B Rigid body equation P Case 2. Share the motion at this point 2 1 ME 316 Handout 2

Solving Kinematics Problem Case 3. 1 2 P1 P2 Relative Translation Equation ME 316 Handout 2

Example Given θ, V0. Find: ω(θ) A B V0 θ 1 2 a ME 316 Handout 2

Solving Kinematics Problem Solution (to be filled) ME 316 Handout 2

Solving Kinematics Problem Solution (to be filled) ME 316 Handout 2

Solving Kinematics Problem Solution (to be filled) ME 316 Handout 2