ENG1011 Chap.13 Frames, Machines and Mechanical Advantage
Frames, Machines and Mechanical Advantage
Frames, Machines and Mechanical Advantage covers Weeks 10 and 11. Frames and machines contain at least one multi-force member, loaded at three or more points or along its length, so unlike truss members their forces need not lie along their axes. The analysis is still equilibrium, as the Week 10 overview emphasises.
The structure is separated at each shared pin, and the pin force on one member is drawn equal and opposite on the other, using the same symbols so the members' equations link together. Any member loaded only at two pins remains a two-force member, whose force runs along the line joining those pins, and spotting these first reduces the number of unknowns. Machines are frames designed to transmit and change forces.
Their mechanical advantage is the ratio of the output force to the input effort, and for a lever it equals the effort arm divided by the load arm, measured from the fulcrum. A higher mechanical advantage is paid for with greater movement at the effort end.
Weeks 10 and 11 are examined with frame and machine problems of increasing complexity, supported by the Week 10 and Week 11 workshop quizzes.
Typical questions ask for a pin force, a support reaction or the output force of a lever system, and a full answer shows each separated member with its own diagram. Week 11 continues with more complex examples, so the skill to build is a reliable routine for splitting a structure rather than memorised cases.
What this chapter covers
- 01
Multi-force members and how frames differ from trusses
- 02
Separating a frame at its shared pins
- 03
Equal and opposite pin forces
- 04
Two-force members inside frames
- 05
Checking the whole frame after solving
- 06
Machines as frames that transmit force
- 07
Mechanical advantage of levers
- 08
Linked levers and combined advantage
Worked example · free
Effort on a first-class lever
- 1Moments about the fulcrum: effort times 1.0 = 500 times 0.2.
- 1Effort = 100 N.
- 1Mechanical advantage = load over effort = 500/100 = 5, equal to the arm ratio 1.0/0.2.
Key terms
- Frame
- A structure containing at least one multi-force member, designed to stay fixed under load.
- Machine
- An assembly of members designed to transmit and change forces, usually with moving parts.
- Multi-force member
- A member loaded at three or more points, or along its length, so its forces may act in any direction.
- Fulcrum
- The pivot about which a lever turns.
Frames, Machines and Mechanical Advantage FAQ
How is a frame different from a truss?
In a truss every member is loaded only at its two end pins, so each force runs along the member. A frame has at least one member loaded at more points or along its length, so its forces can act in any direction and it can bend.
Why separate a frame at its pins?
Each separated member is a rigid body with three equilibrium equations. Drawing the shared pin forces as equal and opposite pairs links those equations, so the unknowns at every pin can be solved, and a whole-frame check confirms them.
What does a mechanical advantage below one mean?
The machine delivers less force than the effort applied, but moves its load further and faster. Levers with the effort between the fulcrum and the load, such as tweezers, work this way, trading force for movement.
How do I find the mechanical advantage of linked levers?
When the output of one lever drives the input of the next, the overall advantage is the product of the individual advantages. Two levers each with an advantage of 3 give 9, provided no force is lost at the connection.
Which member of a frame should I analyse first?
Look for two-force members first, since their force directions are known. Then choose a multi-force member and take moments about one of its pins, so that the unknown components at that pin drop out of the equation.
Exam move
Practise splitting frames until the equal and opposite pin forces are automatic, and always finish with a check on the whole frame. For machines, write the moment equation about the pivot before any numbers and report the mechanical advantage as a ratio.
Rework one frame and one lever question from each of Weeks 10 and 11. Redraw each frame you practise as separate members before writing any equation, and label every shared pin force with the same symbols on both parts.
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