Using the conservation of energy and balance conditions, it is shown that the shape of the pulley on the spring side of a spring balancer takes on a special spiral shape for the case of a fixed pulley on the weight side. Conversely, it is shown that the shape of the pulley on the weight side takes on an involute shape for a fixed pulley on the spring side. It is also shown that design work is simplified by expressing the spring design equation as a maximum potential energy function.

1.
Patent No. 76426, 1926, Japan (in Japanese)
2.
Kobayashi
,
K.
,
1998
, “
New Design Method of the Spring Balancer
,”
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,
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, pp.
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(in Japanese)
3.
Mathematics Society of Japan, 1971, Dictionary of Mathematics, 2nd Edition, 442, Iwanami (in Japanese)
4.
Parker, S., 1984, McGraw-Hill Dictionary of Scientific and Technical Terms, 3rd Edition, 158, 839, McGraw-Hill Book Company
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