1. Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca ENGI 1313 Mechanics I Lecture 35: Analysis of Frames and Machines

2. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 2 Lecture 35 Objective to illustrate the analysis of frames and machines by example

3. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 3 Example 35-01 The compound shears are used to cut metal parts. Determine the vertical cutting force exerted on the rod R if a force of F = 20 lb is applied at the grip G. The lobe CDE is in smooth contact with the head of the shear blade at E.

4. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 4 Example 35-01 (cont.) Draw FBD  GBA  CDE  FRE F = 20 lb F BC AxAx AyAy NENE DxDx DyDy FxFx FyFy NRNR NENE

5. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 5 Example 35-01 (cont.) What FBD and Equilibrium Equations? F = 20 lb F BC AxAx AyAy NENE DxDx DyDy FxFx FyFy NRNR NENE

6. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 6 Example 35-01 (cont.) GBA F = 20 lb F BC AxAx AyAy

7. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 7 Example 35-01 (cont.) CDE F BC NENE DxDx DyDy

8. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 8 Example 35-01 (cont.) FRE FxFx FyFy NRNR NENE

9. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 9 Example 35-02 The kinetic sculpture requires that each of the three pinned beams be in perfect balance at all times during its slow motion. If each member has a uniform weight of 2 lb/ft and length of 3 ft, determine the necessary counterweights W1, W2, and W3 which must be added to the ends of each member to keep the system in balance for any position. Neglect the size of the counterweights.

10. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 10 Example 35-02 (cont.) FBD AA BB CC  Angles? W1W1 AyAy LL AyAy ByBy W2W2 LL CyCy ByBy W3W3 LL  

11. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 11 Example 35-02 (cont.) Beam A W1W1 AyAy LL 

12. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 12 Example 35-02 (cont.) Beam B AyAy ByBy W2W2 LL 

13. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 13 Example 35-02 (cont.) Beam C CyCy ByBy W3W3 LL 

14. ENGI 1313 Statics I – Lecture 35© 2007 S. Kenny, Ph.D., P.Eng. 14 References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_eng mech_1