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0542-4420

Theory of machines

Also listed as: תורת המכונות

Linkages, cams and gears analysed and then synthesised. The course that makes a mechanism something you can specify rather than something you copy.

Semester
Semester A
Weekly hours
4h
Counts as
Core: systems
Interest areas
Mechanical design · Mechatronics and robotics

Comes after

  • Rigid body dynamics
  • Mechanics of solids 1

Opens up

What it covers

Kinematic analysis

  • Mechanisms and kinematic pairs, mobility by Kutzbach and Grübler
  • Grashof's law and kinematic inversions
  • Position, velocity and acceleration of linkages: graphical polygons, instant centres, loop-closure
  • Coriolis component and where students lose marks on it
  • Four-bar and slider-crank, quick-return mechanisms, transmission angle

Synthesis, cams and gears

  • Two- and three-position synthesis, function, path and motion generation
  • Coupler curves, Chebyshev spacing
  • Cams: displacement diagrams, SVAJ, cycloidal and harmonic follower motion, pressure angle, undercutting
  • Gears: involute geometry, interference, contact ratio
  • Gear trains: simple, compound, epicyclic, and their ratios

Forces and balancing

  • Static and dynamic force analysis
  • Flywheels and speed fluctuation
  • Balancing of rotating and reciprocating masses
  • Gyroscopic effects, friction in bearings, clutches, brakes and belts

Results worth carrying out

  • Kutzbach mobility

    DOF=3(n1)2j1j2\mathrm{DOF} = 3(n-1) - 2j_1 - j_2
  • Grashof condition

    s+lp+qs + l \le p + q
  • Balancing a rotor

    mr=0,mrl=0\sum m r = 0, \qquad \sum m r l = 0

Figures worth knowing

  • Four-bar and slider-crank diagrams
  • Velocity and acceleration polygons
  • Cam SVAJ diagrams
  • Involute gear-tooth geometry
  • Epicyclic train schematics

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