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All figures taken from Design of Machinery , 3 rd ed. Robert Norton 2003

MENG 372 Chapter 11 Dynamic Force Analysis. All figures taken from Design of Machinery , 3 rd ed. Robert Norton 2003. Solution using Newton’s Law. Newton’s Law: For planar motion we have:. Center of Percussion (from Ch.10). a i/G. P. R. a i. a G.

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All figures taken from Design of Machinery , 3 rd ed. Robert Norton 2003

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  1. MENG 372Chapter 11Dynamic Force Analysis All figures taken from Design of Machinery, 3rd ed. Robert Norton 2003

  2. Solution using Newton’s Law Newton’s Law: For planar motion we have:

  3. Center of Percussion (from Ch.10) ai/G P R ai aG • The center of percussion(P) is a point on a body which, when struck with a force, will have associated with it another point called the center of rotation(R) at which there will be a zero reaction force

  4. Single Link in Pure Rotation From free body diagram: SF=m2a=FP+F12 ST=Iga=T12 +(R12F12)+(RPFP) Breaking down into components: SFx=m2ax=FPx+F12x SFy=m2ay=FPy+F12y ST=Iga=T12 +(R12xF12y-R12yF12x) +(RPxFPy-RPyFPx)

  5. Single Link in Pure Rotation SFx=m2ax=FPx+F12x SFy=m2ay=FPy+F12y ST=Iga=T12+(R12xF12y-R12yF12x) +(RPxFPy-RPyFPx) Putting into a matrix format

  6. Free Body Diagrams Force Analysis of a Fourbar Linkage

  7. Links 2 and 3 Link 2 Link 3 (F23=-F32)

  8. Link 4 F34=-F43

  9. In One Matrix Equation We have 9 equations and 9 unknowns

  10. Crank Slider Free Body Diagrams:

  11. Crank Slider For Link 4: 8 equations, 8 unknowns

  12. In One Matrix Equation We have 8 equations and 8 unknowns

  13. Inverted Crank Slider (error in the book) Free Body Diagrams: T43 T34=-T43

  14. Links 3 and 4 Link 3 (F23=-F32) Link 4(F34=-F43) T43 T34=-T43

  15. Other equations for F43 We know the direction of F43n F43n T43 F43t q3

  16. Matrix equation with no friction 9 equations, 9 unknowns:

  17. Shaking Forces and Shaking Torque Shaking Force: sum of forces acting on the ground frame FS=F21+F41 Shaking Torque (Ts): reaction torque felt by the ground. Ts=T21=-T12 T21

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