Ch 5. Rigid Body General Motion Multimedia Engineering Dynamics Fixed Axis Rotation Plane Motion Velocities Zero Velocity Point Plane Motion Accelerations Multiple Gears Rot. Coord. Velocities Rot. Coord. Acceleration
 Chapter - Particle - 1. General Motion 2. Force & Accel. 3. Energy 4. Momentum - Rigid Body - 5. General Motion 6. Force & Accel. 7. Energy 8. Momentum 9. 3-D Motion 10. Vibrations Appendix Basic Math Units Basic Equations Sections Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Kurt Gramoll ©Kurt Gramoll

 DYNAMICS - EXAMPLE Two Connected Bars Example Two bars are pinned at one end, and connect with sliding collar at the other end. If the angular velocity of bar AC is clockwise at 3 rad/s, what is the angular velocity of bar BD? Point C slides smoothly along bar BD but is pinned to bar AC 15 cm from point A. . Solution Angular Velocity Since the distance BC is not constant, this problem is well suited for using two frames of reference. Fix the local frame of reference, x-y, on bar BCD so that the motion of C can be easily modeled relative to B, (rC/B)rel. Then the velocity of C is,      vC = vB + Ω × rC/B + (vC/B)rel This equation includes the unknown angular velocity of bar BD, Ω = ΩBC = ΩBD, that is required, and can be determined. The global frame of reference is fixed to the background and is not moving. The velocity of B is zero (it is pinned).      vB = 0 The velocity of C with respect to B, vC/B, is      vC/B = -vC/Bi = -vC/Bcos45I - vC/Bsin45J m/s The velocity of point C, based on the motion of bar AC, in the global coordinate system is      vC = -ωACrAC J = -3(0.15)J = -0.45J m/s The relative position of C with respect to B is     rC/B = 0.15/cos45i = 0.15I + 0.15J m Putting all the terms together, gives     -0.45J = -vC/Bcos45I - vC/Bsin45J + 0 +                     + ΩBDK × (0.15I + 0.15J)      -0.45J = -0.7071vC/BI - 0.7071vC/BJ +               + 0.15ΩBDJ - 0.15ΩBDI Summing the I terms gives,      0.7071vC/B= -0.15 ΩBD      vC/B= -0.2121ΩBD Summing J terms:      -0.45 = -0.7071 (-0.2121ΩBD) + 0.15ΩBD      ΩBD = -1.50K rad/s ΩBD = 1.50 rad/s

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