Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 36 Chp 6: Machines Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

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.

Analysis of Machines Frames and 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 components are equal, have the same line of action, and opposite sense.

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

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

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,

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

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:

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

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

Example: CenterPull Brake

Let’s Work This Nice Problem WhiteBoard Work Let’s Work This Nice Problem Big Ol’ Bolt Cutter ST P9.2.4 => ENGR-36_Lab-19_Fa07_Lec-Notes.ppt For the Cutters with Applied Hand Force, P, Find the Force Applied to the Gripped Bolt

ST P9.1.29

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

Double Toggle Machine

Registered Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 36 Appendix Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

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

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