From the beginning and till the middle of the 19th century there was a demand for a simple and cheap calculation device. Arithmometers and adding machines were too expensive and unreliable. Slide rules didn’t provide required precision necessary for merchants and book-keepers. That is why inventors from different countries (especially from Europe and the USA, where abacus either was not used any more or ever was absent), paid their attention just to the abacus.

From that time different abacus constructions became popular patenting subjects. The information about some abacus patents approved in the USA is presented on this page. The owners of these patents are from the United States and from other countries (including Russia).
J. H. R. Reffelt - Arithmetical Aid, #37825, Mar. 3, 1863
T. Ezersky - Calculating machines, #144523, Nov. 11, 1873
A. C. Wellman - Calculator, #165964, July 27, 1875
G. M. Kendall - Abacus, #9303, May 23, 1876
H. Fitch - Calculators, #232482, Sept. 21, 1880
A.B. Schwenniger - Apparatus for teaching arithmetics, #264572, Sept. 19, 1882
G. W. Bolton and C. H. Tillmeyer - Abacus, #252318, Nov. 9, 1886
C. Pelletier - Ball calculator, #345445, July 13, 1886
E. P. Clark and D. L. Wren - Abacus, #378866, Mar 6, 1888
G. Neuhaus - Abacus, #422612, Mar 4, 1890
H. Stewart - Abacus attachment for Slates, #501379, July 11, 1893
J. Hedgewald and H. Rodelsperger - Apparatus for object lessons in arithmetic, #541787, Jun 25, 1895
L. D. Myers - Abacus, #532282, Jun 25, 1895
B. S. Andrew - Abacus, #580516, Apr. 13, 1897
A. R. Breinl - Apparatus for teaching arithmetic, #604963, May 31, 1898
J. P. Johnsen - Abacus, #637964, Nov. 28, 1899
A. Monachimoff - Abacus, #826732, July 24, 1906
R. C. Bennet - Calculator or Abacus, #1099009, June 2, 1914
A. J. Barber - Abacus Frame, #1441323, Jan. 9, 1923

Even nowadays inventors are still working. Here you can see one of the last patents known to us granted in 1998.

K. Kinnelly - Combination writing board and abacus, #5725380, Mar. 10, 1998

Full descriptions of these patents can be found on USPTO site. Creative inventor mind is still working! Even nowadays inventors from different countries continue to work, - in the USA, Europe and especially in Japan.