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JOURNAL OF TIlE FRANKLIN I N S T I T U T E OF T H E STATE OF P E N N S Y L V A N I A , FOR THE PRO]~[OTION OF THE MECItANIC ARTS. ¥o~. CVlI. JANUARY, 1879. No. 1. THE Franklin Institute is not responsible, as a body, for the statements and opinions advanced by contributors to the Jo~nSAL. AN AUTOMATIC TIT-TAT-TO MACHINE.* FRA%K T. FREELAND, University of Pennsylvania, Class of 1~79. The p r o b l e m of designing a machine which would p l a y one of the games of skill, has been a t t e m p t e d m a n y times. S e v e r a l a u t o m a t a have been c o n s t r u c t e d which would p l a y the game of chess ; but it was always found upon investigation, t h a t their motions were controlled b y a hidden confederate. The infinite number of v a r i a t i o n s in chess r e n d e r s the c o n s t r u c t i o n of a true chess a u t o m a t o n impossible. Mr. B a b b a g e , the i n v e n t o r of the difference engine, in his n i n t h B r i d g e w a t e r treatise, refers to the possibility of c o n s t r u c t i n g an automaton which would p l a y a much simpler game, t h a t of tit-tat-to. A g e n t l e m a n of this city has i n v e n t e d and made some d r a w i n g s of such an automaton, w o r k i n g upon the p r i n c i p l e of a -x'UNIvERSITY OF ])I~NNA., ])HILA., z~5)~ember 9lb. 1S7S. iland you herewith, description and drawings of the automatic Tit-Tat-To Player, exhibited at your last meeting. The invcnti.n displays so much mechanical genius that it cannot hut prove of interest, and perhaps of service, to all mechanicians. Respectfully, W.~. D. MAal(s. De:tr Sir : - - I To J. B. KNIGHT, ESQ., Secretary F r a n k l i n Institute. WHOLE 1gO. VOL CVH.--(TglRD SERIES,Vol. lxxvii.) 1 Freeland-- Tit- Tat- To Machine. [Jour.F r a n k . Inst., movable Jacquard loom card. The machine herein described works upon an entirely different principle, that of a mechanical table, which contains all the possible variations of the game. LOWER PLAN. I! r I Di iL ~i: ~ o WI llJqliilpppl e; l K _ ~____ J o ~ N T,t,,t The game of tit-tat-to is played by two persons. A double cross is drawn upon a sheet of paper. One of the players chooses a cross 11213 (X) for his mark, and writes it in one of the spaces 1-9. 4 5 6 The other player chooses a zero (0), and writes it in one of the remaining spaces, and so on alternately. The 7 - 8- 9- game is won by tile player who first succeeds in getting three of his marks in a row. I f the spaces are all filled before either player gets a row, the game is drawn. The following is an exhaustive analysis of the game of tit-tat-to, for a machine to play the game, under the conditions that the Jan., 1879.] Freeland-- Tit- Tat- To Machine. 3 machine shall always play the best move; and that when the opponent, during the first three moves of each game, wishes to play one of two or four symmetrical moves, he shall take the one having the lowest number. THE OPPONENT BEGINS. [These games will be found upon the Surface of the .Cylinder, lines 1 - - 7 4 inclusive.] THE MACHINE BEGINS. 0 X 0 X 1 2 5 9 °Ix j 3 34678 7 5 25689 2 ........ 0 [ X RBS. i0 7 3 345 4 268 7 7 8 4 3 4 0 0 0 0 0 0 6 0 0 0 2 8 2 5 6 4 9 23589 2 1 45678 8 4 34679 3 5 56789 3 7 46789 3 3 5 8 45689 3 9 1 2 45679 8 5 4 7 3 7 34679 9 8 34678 9 4 289 7 9 3 4 568 5 4 3 469 6 3 9 678 8 9 4 6 689 4 9 468 8 ,) 5 7 467 5 3 6 469 3 365 7 6 0 0 0 0 0 0 0 0 4 0 0 0 0 0 8 9 0 0 0 0 0 4 6 0 0 0 0 0 0 0 0 0 4 Freeland-- Tit- Tat- To Machine. [Jour.F,'a,,k. rnst., The method oF transforming this symbolic table into a meehanioal one, will be obtained by a comparison of it with the Surface of the 63jlinder, beginning at line 75. There are one hundred and fifty lines upon the cylinder. The omitted ones may be obtained from the latter part of the above table. Our 1st, 2d, 3d and 4th moves in any game are set down in the columns T I, II, I I I and IV. Each column contains nine vertical lines. The figure ] is represented by a pin upon the first line; 2, by a pin upon the second line, etc. The machine's answering moves are set down in the column U, upon the same horizontal line as ours. Whenever its move gives it three in a row, another pin is put upon the line U0. The row of pins Ux affords a hold to a catch. When the machine begins, its first move is set down in the column S. DESCRIPTIO~.~In the Lower .Plan, the cylinder D is represented, its surface being prepared as described above. The cord, weight ~EcTION S. and pulley p, give it a tendency to turn toward us. In front of it are the two cross-beams or ways W W. On them the carriage I runs. The cord P , running over a pulley to a weight, gives the carriage a tendency to move to the right. The carriage has a catch C~ which engages with four pins set in a groove in one of the ways. Whenever the catch C is pushed, the carriage 2-moves a space to the right, equal to one column of the table. The wire 0 is to draw it back to its first position. On the carriage are nine sliders, T 1-9. When they move forward, they engage with the pins upon the cylinder. T 1 , 2 and 5 have the pins Z 1, 2 and 5 in them, which project below the carriage. A platform is secured to the ways at the left. On it are the Jan., 1879.] Freeland-- Tit- Tat- To Machine. 5 sliders S 1, 2 and 5, having in them the pins Q 1, 2 and 5, which project below the platform. Supported on a bracket, under the platform, are the flat, horizontal cams Y 1, 2 and 5. When the carriage is in its first position, the pins Q 1, 2, 5 and Z 1, 2, 5 engage with these cams. They are of such a shape, that when the slider T 1, 2 or 5 moves backward, the pin Z 1, 2 or 5 rubs over the pointed end of the cam Y 1, 2 or 5, and so pushes S 1, 2 or 5 forward. At the right is secured to the ways a platform, on which are the sliders Ux, 1-9, 0. The slider U~, by engaging with the row of UPPER ~a~elto.. , .t PLAN. , , ~z, , . : ~ , , , ~*, , , t ~ l a c h e s . o pins Ux, locks the cylinder. U 1-9 discover the answering move. U0 determines the striking of the bell. These sliders are set at a higher level than the others, so that when they move forward, they impinge upon the pins, instead of going under them. K i s a horizontal lever, pivoted at its centre. S 1, 2, 5 and Ux have in their ends bent wires, M a n d N, so that when S 1, 2 or 5 moves forward, K pulls Ux backward. J is a vertical leaf, pivoted at its lower 6 Freeland-- Tit- Tat- To Machine. [ao,r. Frank. Inst., corners, and connected by a double bell-crank with the lever H 1, as shown in Section S. When H 1 is pushed forward, J d r a w s out the catch Ux and the sliders S 1, 2 and 5. q is a vertical leaf, pivoted at its lower corners. When it moves toward the cylinder, it releases the carriage by striking the catch C. q has secured to it an arm with a pin in it, as shown at V, Section ~£ SECTION SEC' T. I~)N U. .?iX I "~&t In the Upper _Plan, is shown a portion of the board. I t has nine openings in it. Under them move the ares A 1-9. There is a cross (X) on one end of each, and a zero (0) on the other. These arcs are secured to the vertical leaves L 1-9, which are pivoted at their upper corners. B y long wire teeth they gear into the sliders T 1-9 in such a way, that they do not get out of gear when the carriage moves to the right or left. See the Elevation and ~ection T. In Section U, the levers Z r 2 and ab are represented. They are pivoted on each side of the platform at b, and firmly united by a .Freelandw Tit Tat- To Machine. Jan., 1879.] cross-piece under the platform. On the lower end of ab is fastened an inclined plate V. When the lever H 2 moves backward, the plate V lifts the arm of ~ by the pin on it, and so releases the carriage. From ab to H 2 at the point a runs a stout wire. On it are strung the vertical levers Xx, 1-9, 0. Their upper ends are held back against the plate F, which serves as a fulcrum, by the H EL~-~-~ON. m R A 7 8 9 IIIIII L 9 . . 11 I,,I I( / . . . . | . "' L ........... , ' _~ . . . . . . . . I I~ L~ L f I J iI [i J ,, _~ . . . . . . . . . . . . " ............ 1 ii , • J I I I i ql / I J__, . . . . . . . . . ,11 -- ,, III :I : I Ill :I ! J ~.&l. springs as shown. Their lower ends are geared into the sliders Ux, 1-9, 0. When H 2, containing the point a, moves forward, the levers Xx, 1-9, 0 move forward, their upper ends being their fulcrums, pushing ihe sliders Ux, 1-9, 0 forward. If one of these impinges on a pin, it stops, and becomes the fulcrum of the X belonging to it. Then the upper end of that X goes forward, elongating the spring. The slider Ux has a slot at its point of gearing, so that when it is carried forward it is left there. When the upper ends of Freelan d - - Tit- Tat- To Machine. [Jour.Frank. Inst., X 1-9 move forward, they strike the r o d s / ~ 1-9, which are hooked to the vertical leaves B 1-9, pivoted at their lower corners. These are connected by the wire links E 1-9 with the arcs. When the upper end of X 0 goes forward, it causes a bell to strike. OeERATI0~.--The machine is wound up by setting all the arcs at their middle position, so that neither mark appears; then push H 1 and wind up the cylinder by a key at the left; push H 2 and it is locked ; and lastly draw the carriage into its first position. We make our move by putting an instrument like an awl into one of the holes of the arcs, and so moving it that the cross appears. Suppose we move 2, then slider T 2 goes forward. Release the cylinder from the catch by pushing H 1. The cylinder turns until the pin at T I 2, line 22, strikes the slider. On pushing H 2 forward, Jan., l s ~ 9 . ] Freeland-- Tit- Tat- To Machine. 9 the pin at U 5 will stop the slider U 5, and X 5 will push R 5 and B 5 forward. Then the w i r e E 5 from B 5 t o A 5 will so move the are that the zero (0) will appear at the opening 5. At the same time the slider Ux will move forward and lock × ×io the cylinder. When H 2 comesback, the car- - - ! ~ - riage will move into position II, opposite the - - - - i - column T II. Suppose we then move 1, the ! oiX 0 c y l i n d e r w i l l s t o p a t l i n e 2 8 , and the machine X Xi 0 .... moves 8, the carriage taking position III. If O OO__ we now move 7, the cylinder will stop at line 24, the machine moves 4, and the carriage x ! O - - X X 0 takes position IV. If we move 6, the cylinder X X/0 ~- ~- ~ stops at line 25, and the machine moves 8. [If -0-]-6-~ ~- - we had moved 8 or 9, the cylinder would have -X -0- - stopped at line 26, the machine would have moved 6 and won. The pin on U0 causing the bell to strike.] Finally we move 9, and the game is drawn. The machine is thenwound up. If we wish the machine to begin, we move one of the arcs so that the zero appears. Suppose that we so move 1. The slider T 1 is moved backward, hence S 1 is pushed forward by :Y 1, and K pulls the catch from the cylinder, which turns until the pin at S 1, line 75, strikes the slider S 1. Then we make our move, suppose it to be 2. On touching H 1, the cylinder remains at line 75, and on pushing H 2, position II. Now, if we move 9, the cylinder stops at line 76, and the machine moves 7, the carriage taking position III. If we then move 0 X 0 4, the cylinder stops at line 77, the machine 0 X1X -~]~-moves 3 and wins, the bell proclaiming the -0-i-0-fact; but, if we move 8, 6 or 87 the cylinder stops at line 79, the machine moves 4. So it O - I - - wins in either case. This machine, the first one ever constructed, was built in the summer of 1878, and exhibited at the Franklin Institute, October 16, 1878. It is now at the University of Pennsylvania, where, since its final adjustment, it has played a large number of games without losing a single one. PtIILADELPHIA,November 8tit, 1878.