Gottfried Wilhelm Leibniz and his calculating machine

1
Gottfried Wilhelm Leibniz and his calculating
machine

• report by Torsten Brandes

2
Chapter 1

• Construction of mechanical calculating machines

3
Structure of a mechanical calculating machine

• counting mechanism

two counting wheels
4
counting mechanism

• Every counting wheel represents a digit.
• By rotating in positive direction it is able to
  add, by rotating in negative direction it is able
  to subtract.
• If the capacity of a digit is exceeded, a carry
  occurs.
• The carry has to be handed over the next digit.

5
counting mechanism
S lever Zi toothed wheel
dealing with the carry between two digits
6
Chapter 2 calculating machines bevore and after
Leibniz

• 1623
• Wilhelm Schickard developes a calculating machine
  for all the four basic
• arithmetic operations. It helped Johann Kepler to
  calculate planets orbits.
• 1641
• Blaise Pascal developes an adding- and
  subtracting machine to maintain
• his father, who worked as a taxman.
• 1670 - 1700
• Leibniz is working on his calculator. 
• 1774
• Philipp Matthäus Hahn (1739-1790) contructed the
  first solid machine.

7
Leibniz calculating machine.

• Leibniz began in the 1670 to deal with the topic.
• He intended to construct a machine which could
  perform the four basic arithmetic operations
  automatically.
• There where four machines at all. One (the last
  one) is preserved.

8
stepped drum
A configuration of staggered teeth. The toothed
wheel can be turned 0 to 9 teeth, depending of
the position of this wheel.
9
four basic operations performing machine by
Leibniz
10
Skizze
drawing W. Jordan

• H crank
• K crank for arithmetic shift
• rotation counter

11
Functionality

• Addition
• partitioning in two tacts
• Addition digit by digit, saving the occuring
  carries with a toothed wheel.
• Adding the saved carries to the given sums,
  calculated before.

12
(No Transcript)
13
Subtraction.

• Similar to adding.
• The orientation of rotating the crank has to be
  turned.

14
(No Transcript)
15
Multiplication (excampel)

• was possible by interated additions
• 32.44875
• Input of 32.448 in the adjusting mechanism.
• Input of 5 in the rotation counter.
• Rotating the crank H once. The counting mechanism
  shows 162.240.
• Rotating the crank K. The adjusting mechanism is
  shifted one digit left.
• Input of 7 in the rotation counter.
• Rotating the crank H once. The counting mechanism
  shows 2.433.600.