A Taxonomy of Planimeters        Charles Care       September 2004
What is a Planimeter?• “Planimeters are instruments for the determination by mechanical  means of the area of any figure.” ...
Where Planimeters Fit In                                                       Engineering                                ...
Pre-1851 PlanimetersVarious isolated∗ developments •   Hermann (1814) •   Gonella (1824) •   Oppikofer (1836) •   Wetli (1...
Post-1851 PlanimetersAn explosion in manufacture •   Amsler (1854) – 12,000 sold by 1892 •   Maxwell (1855) •   Thompson (...
Variable Gears• All mechanical planimeters use some kind of variable gear.• This is archetypally a wheel rolling on a disc...
Variable Gear: Cone and Wheel
Variable Gear: Disc and Wheel
Variable Gear: Sphere and Sphere
Variable Gear: Disc, Ball and Cylinder
Variable Gear: Wheel and Cylinder
Variable Gear: Wheel and Sphere
But what about Polar Planimeters?
Or this one?
Difficulties           Wheel                        SphereCone       Hermann Gonnella OppikoferDisc       Wetli Coradi      ...
Difficulties           Wheel                        SphereCone       Hermann Gonnella OppikoferDisc       Wetli Coradi      ...
Classification by the tracing mechanism• System used by Henrici in 1894• Three basic types   I Orthogonal  II Polar-Coordin...
Type I Orthogonal         • Position generated by varying           two lengths         • Type of early planimeters       ...
Type II Polar-Coordinate             • Position generated by varying               one lengths and one rotation           ...
Type III Amsler (Polar Planimeter)                  • Position generated by varying                    two rotations      ...
Another classificationIs the area recorded by slipping or rolling∗.∗ Used   by Hele Shaw
Summing UpSeveral ‘characteristics’ used to classifyplanimeters • Classification by components   – Difficult to separate pola...
A Taxonomy of Planimeters        Charles Care       September 2004
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A Taxonomy of Planimeters

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Paper given at Annual History of Computing Seminar, University of Warwick, September 2004.

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A Taxonomy of Planimeters

  1. 1. A Taxonomy of Planimeters Charles Care September 2004
  2. 2. What is a Planimeter?• “Planimeters are instruments for the determination by mechanical means of the area of any figure.” (Encyclopedia Britannica 11th Ed.)• An integrating machine.• A component of the differential analyser.
  3. 3. Where Planimeters Fit In Engineering Machines Electronic Analogue MomentNapier’s Bones Planimeters Watt−hour Integraphs meters Differential AnalysersAstrolabes Planimeters Mechanical Integrators Mathematical Instruments
  4. 4. Pre-1851 PlanimetersVarious isolated∗ developments • Hermann (1814) • Gonella (1824) • Oppikofer (1836) • Wetli (1850) • Sang (1850)∗ Some sources indicate a link between Gonella and Oppikofer
  5. 5. Post-1851 PlanimetersAn explosion in manufacture • Amsler (1854) – 12,000 sold by 1892 • Maxwell (1855) • Thompson (1861-1864) • Coradi & Ott (Late 19th Century) • Developments in Uk and US
  6. 6. Variable Gears• All mechanical planimeters use some kind of variable gear.• This is archetypally a wheel rolling on a disc but can be many other things Wheel Sphere Cone Hermann Gonnella Oppikofer Disc Wetli Coradi Thomson Sphere Boys Maxwell Cylinder Boys Surface Amsler Coradi etc.
  7. 7. Variable Gear: Cone and Wheel
  8. 8. Variable Gear: Disc and Wheel
  9. 9. Variable Gear: Sphere and Sphere
  10. 10. Variable Gear: Disc, Ball and Cylinder
  11. 11. Variable Gear: Wheel and Cylinder
  12. 12. Variable Gear: Wheel and Sphere
  13. 13. But what about Polar Planimeters?
  14. 14. Or this one?
  15. 15. Difficulties Wheel SphereCone Hermann Gonnella OppikoferDisc Wetli Coradi ThomsonSphere Boys MaxwellCylinder BoysSurface Amsler Coradi etc.
  16. 16. Difficulties Wheel SphereCone Hermann Gonnella OppikoferDisc Wetli Coradi ThomsonSphere Boys MaxwellCylinder BoysSurface Amsler Coradi etc.
  17. 17. Classification by the tracing mechanism• System used by Henrici in 1894• Three basic types I Orthogonal II Polar-Coordinate (not Amsler-type) III Amsler-type (commonly called Polar Planimeters)
  18. 18. Type I Orthogonal • Position generated by varying two lengths • Type of early planimeters – Wheel & Cone – Wheel & Disc – Sphere & Sphere
  19. 19. Type II Polar-Coordinate • Position generated by varying one lengths and one rotation • Very few constructed – Wheel & Cylinder – Wheel & Sphere – Sphere & Sphere
  20. 20. Type III Amsler (Polar Planimeter) • Position generated by varying two rotations • All large-scale productions belong to this class – Wheel & Disc (Coradi) – Slipping Wheel
  21. 21. Another classificationIs the area recorded by slipping or rolling∗.∗ Used by Hele Shaw
  22. 22. Summing UpSeveral ‘characteristics’ used to classifyplanimeters • Classification by components – Difficult to separate polar and orthoganal • Henrici’s classification – Useful to understand the geometry of the various planimeters • Hele Shaw’s classification – But need to consider pure rolling systems as well
  23. 23. A Taxonomy of Planimeters Charles Care September 2004

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