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

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

3. Center of Percussion (from Ch.10) 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 a i/G aGaG aiai R P

4. Single Link in Pure Rotation From free body diagram:  F=m 2 a=F P +F 12  T=I g  T 12 +(R 12  F 12 )+(R P  F P ) Breaking down into components:  F x =m 2 a x =F Px +F 12x  F y =m 2 a y =F Py +F 12y  T=I g    R 12x F 12y -R 12y F 12x )  +  R Px F Py -R Py F Px )

5. Single Link in Pure Rotation  F x =m 2 a x =F Px +F 12x  F y =m 2 a y =F Py +F 12y  T=I g    R 12x F 12y -R 12y F 12x ) +  R Px F Py -R Py F Px ) Putting into a matrix format

6. Free Body Diagrams Force Analysis of a Fourbar Linkage

7. Links 2 and 3 Link 2 Link 3 (F 23 =-F 32 )

8. Link 4 F 34 =-F 43

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: T34=-T43 T43

14. Links 3 and 4 Link 3 (F 23 =-F 32 ) Link 4(F 34 =-F4 3 ) T34=-T43

15. Other equations for F 43 We know the direction of F 43n T 43 F 43n F 43t 33

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 F S =F 21 +F 41 Shaking Torque (T s ): reaction torque felt by the ground. T s =T 21 =-T 12 T 21