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Analysis of Frames & Machines: Practical Examples & Equilibrium Equations

Learn through practical examples the analysis of frames and machines, how to draw free body diagrams, and apply equilibrium equations. Includes determining cutting forces and counterweights.

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Analysis of Frames & Machines: Practical Examples & Equilibrium Equations

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  1. ENGI 1313 Mechanics I Lecture 35: Analysis of Frames and Machines

  2. Lecture 35 Objective • to illustrate the analysis of frames and machines by example

  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. Example 35-01 (cont.) • Draw FBD • GBA • CDE • FRE FBC F = 20 lb Ax Ay NE Dy FBC Fy Dx Fx NR NE

  5. Example 35-01 (cont.) • What FBD and Equilibrium Equations? FBC F = 20 lb Ax Ay NE Dy FBC Fy Dx Fx NR NE

  6. Example 35-01 (cont.) • GBA FBC F = 20 lb Ax Ay

  7. Example 35-01 (cont.) • CDE Dy FBC Dx NE

  8. Example 35-01 (cont.) • FRE NE Fy Fx NR

  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. Example 35-02 (cont.) • FBD • A • B • C • Angles? L W1  Ay Ay L L   By W2 W3 By Cy

  11. Example 35-02 (cont.) • Beam A L W1  Ay

  12. Example 35-02 (cont.) • Beam B Ay L  W2 By

  13. Example 35-02 (cont.) • Beam C L  By W3 Cy

  14. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1

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