Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

1. Engineering 36 Chp6:Machines Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Introduction: MultiPiece Structures • For the equilibrium of structures made of several connected parts, the internal forces as well the external forces are considered. • In the interaction between connected parts, Newton’s 3rd Law states that the forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. • Three categories of engineering structures are considered: • Frames: contain at least one multi-force member, i.e., a member acted upon by 3 or more forces. • Trusses: formed from two-force members, i.e., straight members with end point connections • Machines: structures containing moving parts designed to transmit and modify forces.

3. Analysis of Machines • Framesand Machines are structures with at least one multiforce member. Frames are designed to support loads and are usually stationary. Machines contain moving parts and are designed to transmit & modify forces. • A free body diagram of the complete frame is used to determine the external forces acting on the frame. • Internal forces are determined by dismembering the frame and creating free-body diagrams for each component. • Forces on two force members have known lines of action but unknown magnitude and sense. • Forces on multiforce members have unknown magnitude and line of action. They must be represented with two unknown components. • Forces between connected componentsare equal, have the same line of action, and opposite sense.

4. Pin Equilibrium • Consider Actions of Members AD & CF on Pin-C • Member CF • Pulls Pin RIGHT • Pushes Pin UP • Member AD • Pulls Pin LEFT • Pushes Pin Down • FBD

5. Pin Equilibrium • Note that Pin-C is in Equilibrium • By ΣFx = ΣFy = 0 • The forces on the MEMBERS caused by the Pin are Equal and Opposite as Predicted by Newton’s 3rd Law

6. Machines • Machines are structures designed to transmit and modify forces. Their main purpose is to transform input forces into output forces. • Given the magnitude of P, determine the magnitude of Q. • Create a free-body diagram of the complete machine, including the reaction that the wire exerts. • The machine is a nonrigid structure. Use one of the components as a free-body. • Taking moments about A,

7. Example: CenterPull Brake • For the Center-Pull Bicycle Brake shown at right find Normal Force Exerted by the BrakePad on the Rim • Neglect the brake-opening Spring Force

8. Example: CenterPull Brake • There is a Single cable connecting Pts B, G, & C • Thus TGB = TGC • The FBD for the Cable Connector • The Forces at the connector are CONCURRENT → Particle Applies • Take the ΣFy = 0 • Note:

9. Example: CenterPull Brake • The ΣFy = 0 at G • Use Trig & Geometry to find TBCG • The FBD for Brake Arm BAE

10. Example: CenterPull Brake • Find Fnormal by ΣMA = 0 • Note • Use F∙d to find Moments about A

11. Example: CenterPull Brake 70 N

12. WhiteBoard Work Let’s WorkThis NiceProblem Big Ol’ Bolt Cutter • For the Cutters with Applied Hand Force, P, Find the Force Applied to the Gripped Bolt

14. Pliers (4-pc Structure) • AB is TWO-Force Member

19. Double Toggle Machine

20. Engineering 36 Appendix Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

21. Friction-Filled Bearing • Consider Non-Frictionless Bearing • From the Diagram • r ≡ Brg Radius • F ≡ Brg Support Force as determined by Static Analysis • If the Brg has non-negligible Friction the Moment that OPPOSES rotation r O F

22. Friction-Filled Bearing • The Rotation Resisting Moment: • Where • µ ≡ the Bearing’s COEFFICIENT of FRICTION • µ Discussed in Detail in Chp08