Few clocks with minute and hour

Transcription

1 The Development of the One-Movement-Balanced-Hands Clock by Rubens A. Sigelmann (WA) Introduction Few clocks with minute and hour balanced hands (BH) that are independent from each other have been built in the past. Each one of the BHs has a clock movement. The balanced hands clock discussed here uses one movement in the minute hand; the hour hand is driven by the minute hand. I discuss a balanced independent-hand clock that contains a movement in each hand in the April 2002 Bulletin. A brief review of the operation principle of balanced hand clocks that pertain to both types of clocks will be presented here. For a more detailed discussion on BHs, see The Balanced- Independent-Hand Clock by Rubens A. Sigelmann, NAWCC Bulletin, April 2002, Vol. 44, No. 337, pp The first reference for this type of clock, to the best of the author s knowledge, is U.S. Patent 78,972, dated June 16, 1868, issued to Charles King. On August 18, 1914, U.S. Patent 1,107,947 was granted to Harrison W. Hicks. His patent describes a clock with a single clock movement that is a component of the minute BH in the same sense as C. King s patent. The minute BH drives the hour hand by a conventional 2-pinion, 2-gear arrangement. Because the Hicks clock is the other clock that uses only one movement and a balanced hand, the principle of operation of the Hicks clock is also reviewed here. Circa 2000, the idea of a clock that has two balanced hands but only one clock movement started to emerge in my brain. It took about two years to build the prototype (Figure 1). Obviously, the objective of a prototype is to test an idea; therefore its mechanism is exposed for examination. I then built two one-movement mystery clocks. In the first one, I tried to implement the concept of the prototype in an attractive mystery clock (Figure 2). I built the frame of the clock and the balanced hands with bent rosewood. Figure 1. Prototype of the one-movementbalanced-hands clock. Figure 2. First version of mystery one-movement-balanced-hands clock. Figure 3, below. Second version of mystery one-movement-balanced-hands clock. I finished the construction of this clock in 2006; and it worked well. With the experience I gained, I built the second version of this type of clock (Figure 3). I made several improvements that I discuss here. The construction of the second clock took another three years (Figure 3). I intended to enter this clock in the NAW- CC Crafts Contest in Class 5-Experimental Timepiece Designs, in the 2009 National Convention, Grand Rapids, MI. However, the so-called improved clock worked erratically and I ran out of time to have it fixed. So I switched the hands between the first and the second mystery clocks (Figure 4). This clock worked well and was awarded first prize in Class 5. After I returned from the National Convention I adjusted the improved clock. It has been working well since. NAWCC Watch & Clock Bulletin August

2 Figure 4. Mystery clock 1 st prize 2009 NAWCC Craft Contest, Class 5. Note the hands are different from clock in Figure 3. Principle of operation of balanced hands (BH) All BHs with one movement may be represented by the simplified Figure 5. If in Figure 5 the clock movement and the mass m 3 are replaced by gear 1 and its attached weight as shown in Figure 9(b), this hand will still be a balanced hand. The function of gear 2, as explained later, is to rotate gear 1 when the minute hand turns. The BH turns freely around an axis at the point of suspension. Mass m 1 represents all the mass above the point of suspension and l 1 the distance of the center of mass (CM) of this mass to the point of suspension. Similarly, m 2 represents all mass (m 3 excluded) below the point of suspension and l 2 the distance of the CM of this mass to the point of suspension. The additional mass (or weight) m 3 is connected to the minute or hour arbor of the clock movement, depending on whether the BH is the minute or the hour BH. Since the clock movement is mounted in the BH in reverse, an observer looking at the front of the BH would see m 3 turning along the dotted circle of radius r shown in Figure 5 in the counterclockwise direction. A wellbalanceed BH satisfies the condition m 1 l 1 = (m 2 +m 3 )l 2. In the construction of a BH, provisions are made to adjust l 1 such that the above condition is satisfied. As Figure 5 indicates, in a well-balanced BH, m 3 always points down in the directions of the gravity. Thus, if m 3 turns an angle β in the counterclockwise direction, the BH turns an equal angle α in the clockwise direction so that m 3 points down in the direction of gravity. The Hicks clock Figure 6 is the second page of the Hicks patent. To facilitate the explanation of the operation of the Hicks clock, Fig. 2 of the patent is redrawn as Figure 7. This figure has the essen- Figure 5. Diagram to explain the operation of balanced hands. tial elements to explain the differences between the Hicks clock and the onemovement BH clock I developed. The minute hand rotates freely about the fixed pivot shaft (Figure 7). The small pinion P 1 (9 in Fig. 2), which is secured to the minute hand, meshes with large pinion P 2 (10 in Fig. 2). Pinion P 2 and the small pinion P 3 (13 in Fig. 2) are affixed to the same pivot shaft (11 in Fig. 2) at each side of the fixed bracket (12 in Fig. 2). This shaft rotates freely through the passage in the bracket (12 in Fig. 2). Pinion P 3 meshes with larger pinion P 4 (14 in Fig. 2). Pinion P 4 is secured at one end of the sleeve (15 in Fig. 2). The hour hand (16 in Fig. 2) is secured at the other end of the sleeve. Hicks does not mention in his patent how to calculate the number of teeth in each of the four gears (pinions). Because the minute and the hour hands are concentric, the number of teeth has interesting implications that will be discussed later. The one-movementbalanced-hands clock Figure 8 is a sketch of the first one-movement-balancedhands mystery clock. In this clock, the minute balanced hand has the clock movement. A weight is attached to the arbor of the clock movement that usually carries the minute hand. If the weight turns in the counterclockwise direction, the minute balanced hand turns in the clockwise direction. This hand is fixed to the first pivot shaft by the spacers S 6 and S 7. The first pivot shaft turns freely inside the plastic housing rotating about two ball bearings. The balanced hour hand does not have a clock movement. Instead, it has a unique and novel system of two gears (called first and second gears). The second gear is fixed by spacers S 3 and S 4 to the first pivot shaft and meshes with the first gear. The first gear can turn freely around its pivot shaft. The first gear has a ball bearing that is not seen in Figure 8. A weight is secured to the first gear. The balanced hour-hand assembly can turn freely around the first pivot shaft about the ball bearings B 1 and B 2. All the spacers S 1, S 2, S 5, and the spacers mentioned above are used to apply axial pressure to the minute BH and to 448 August 2010 NAWCC Watch & Clock Bulletin

3 Figure 6, left. Second page of H. W. Hicks US Patent 1,107,947. Figure 7, above. Schematic redrawing of Fig. 2 of Hicks Patent. Figure 8, below. Schematic representation of the clock in Figure 2. the second gear. Thus the minute BH and the second gear are fixed to the first pivot shaft and rotate together. The positions of the minute and hour BHs are adjusted such that when the minute BH indicates 12 o clock, the hour BH indicates exactly an integer hour. Then the two knurled nuts at the extremities of the pivot shaft are tightened. I do not wish to suggest that the development of this clock went smoothly and was always under my control. One example of a stumbling block was my choice of the ratio (R) representing the number of first gear teeth to second gear teeth. When I built the prototype, it was obvious to me that this ratio should be 12. To my great disappointment I found when the minute BH turned 12 turns, the hour BH instead of a complete turn was short by one hour (11/12 turn). I NAWCC Watch & Clock Bulletin August

4 Figure 9, above. Diagram to explain the operation of the hour balanced hand and the calculation of the ratio of the number of teeth of the first gear to the number of teeth of the second gear. Figure 10, right. Diagram to explain the arrangement of gears for concentric minute and hour hands. spent a couple days trying to find a mechanical flaw in the clock but to no avail. Finally I had to make the following calculations. In Figure 9 the hour BH is represented only by the components pertinent to the calculations. The details of the hour BH was already shown in Figure 8. It makes no difference when the minute hand turns an angle whether the hour hand is held and then released or the hour hand is free to turn. The hour hand will turn in both cases exactly the same angle. Let us assume the hour BH represented in Figure 9a is held in the vertical position (12 o clock), while the minute BH is turned by angle α in the clockwise direction. Since gear 2 is rigidly connected to the minute BH, it also rotates an angle α. Then gear 1 would turn by an angle γ = α/r in the counterclockwise direction. Now the hour BH is released and gear 2 remains in the same position (Figure 9b). The initial position of the hour BH is shown in Figure 9b as the dotted hand. Because this hand is balanced, it turns around point P by an angle β until the weight aligns with the force of gravity, i.e., vertical. However, if the hand turns by an angle β in the clockwise direction while gear 2 remains in the same position, gear 1 turns by an angle β/r in the clockwise direction. So the angle β in the counterclockwise direction, as shown in Figure 9b, is equal to the counterclockwise angle γ minus the clockwise angle β/r. Let us write an equation to represent the statement above: β = - β R We found that γ = α/r. Furthermore, since gear 2 turns together with the minute BH, α indeed indicates the minutes. Then in a 12-hour clock β = α/12. Substituting in the above equation, we obtain α = α - α 12 R 12R from which we conclude that R = 11. This ratio solved one of the stumbling blocks, except that I got stuck with a large number of gear pairs with ratio 12 (10 and 120 teeth). The ratios of teeth of the four gears in the Hicks clock As mentioned above, Hicks does not discuss the number of teeth in the four gears of his clock. His arrangement of teeth is a conventional one used by most timepieces; the hour and minute hands are concentric. Figure 10 is a schematic diagram of this arrangement. Gear G 1 is connected to the minute axis by a clutch system (the simplest is by friction) that permits setting the time in the timepiece. The gear G 4 turns at 1/12 of the speed of gear G 1. If all the gears have the same pitch, there are three possibilities for how this can be achieved: (1) the ratio of number of teeth N 2 of gear G 2 to the number of teeth N 1 of gear G 1 is 3, and the ratio of number of teeth N 4 of gear G 4 to the number of teeth N 3 of gear G 3 is 4 (it could be vice-versa, but the first option is preferable because then the radius R 1 is larger than R 3, which makes the clutch system easier to build); (2) the ratio of number of teeth N 2 of gear G 2 to the number of teeth N 1 of gear G 1 is 1, and the ratio of number of teeth N 4 of gear G 4 to the number of teeth N 3 of gear G 3 is 12; (3) the ratio of number of teeth N 2 of gear G 2 to the number of teeth N 1 of gear G 1 is 1.5, and the ratio of number of teeth N 4 of gear G 4 to the number of teeth N 3 of gear G 3 is 8. Because the hour and the minute hands are concentric, from Figure 10 it can be seen that: R 1 + R 2 = R 3 + R 4 (1) The radius of a gear is proportional to the number of teeth. 450 August 2010 NAWCC Watch & Clock Bulletin

5 Figure 11. Hour BH of the first mystery clock. In the first arrangement, R 2 = 3R 1 and R 4 = 4R 3 substituting in the equation (1 ) above 4R 1 = 5R 3 or R= 4 R 1. For instance, if we choose N 1 = 10 then N 3 = 8, N 2 = 30, and N 4 = In the second arrangement, R 2 = R 1 and R 4 = 12R 3 are substitued in the above equation (1) 2R 1 = 13R 3 or R 3 = 2 13 R For instance, if we choose N 1 = 39 then N 3 = 6, N 2 = 39, and N 4 =72. This arrangement is seldom used. In the third arrangement R 2 =1.5R 1 and R 4 = 8R 3. Substituting in the above equation (1) 2.5R 1 = 9R 3 or R 3 = R 1 For instance if we choose N 1 = 36 then N 3 = 10, N 2 = 54, and N 4 = 80. Although this establishes an important rule about how to design concentric hands using gears with the same pitch, I did not find in the horological literature any reference to it. IF the Hicks clock should be built today, the four gears should be arranged according to the first arrangement. 1 The second onemovement BH mystery clock There are two problems with the first mystery clock. The first problem in the design was that the second gear is inside the box that contains the first gear. This is shown in Figure 11. This imposes restrictions on the shape of the hour BH and result is not esthetically pleasant. The second problem is that the BH is very sensitive to misalignment. Misalignment happens when the CM of m 1, CM of m 2, and the point of suspension are not in the same straight line (Figure 5). To be in the same line requires a construction precision difficult to achieve. To restore the proper balance of the hand, additional weights are attached by trial and error inside the box. In the second mystery clock the first problem was solved by replacing the second gear with three identical gears as shown in Figures 12 and 13. Figure 12 clearly shows that the first pivot Figure 12. Hour BH of the second mystery clock. Figure 13. Detail of the mechanism to convert minute to hour in the second mystery clock. shaft and the last of the three gears are outside of the box. Figure 13 gives a better view of the modified system of gears. The larger gear has 88 teeth and the 3 pinions have 8 teeth. The larger gear was made by Philip J. Johansen. The second problem was resolved by splitting the hands and connecting them by a hinge mechanism (see Figure 14). In a well-balanced hand when the weight is exactly aligned with the direction of the hand, the BHs should be exactly at the 6 or 12 o clock position. However, because of the required precision in the construction this is NAWCC Watch & Clock Bulletin August

6 Figure 14. The minute and hour BHs showing the hinge mechanism. rarely achieved. Then the BH is adjusted by releasing the nut in the hinge mechanism and turning the box in one direction or another while making sure the weight is exactly aligned with the direction of the hand. When the adjustment is completed, the nut is tightened. Conclusions and Observations For good stability of the clock it is necessary to have one of the BHs in the front and the other in the back. Then the dial must be transparent to see the two BHs. The first clock dials were glasstempered 10¼" dinner plates. Despite the advice of skilled glass craftsmen who told me that tempered glass cannot be drilled, I tried. The result was three explosive breakages. So I purchased a 12" tempered pan glass lid, removed the outside rim and the knob, and used the center knob hole to install the plastic housing journal. Blancheros Glass & Etching, Inc., etched the computer-generated dial pattern. In this type of clock one may choose to have the minute or the hour BH in front. I prefer the hour BH in the front and the minute BH in the back. The rim of the clock dial is made of laminated rosewood. Strips of 0.1" are band saw cut from a piece of rosewood and bent in hot water. It takes about one week to bend a strip. Several times I paid a high price for my impatience: when one tries to go faster than the process allows, one hears a disgusting crack noise. That is the signal to start all over again. To prevent deformation of the rim, the rim is made with two layers glued together with epoxy. The box of the hands is made with one layer from a strip of 0.05" thickness. It takes longer to bend the boxes because of the smaller curvature radius. Obviously, the minute hand drives the hour hand. However, the hour hand in principle does not drive the minute hand. If the hour hand is displaced from its position of equilibrium, it oscillates for a while and returns to the position of equilibrium without disturbing the minute hand. The qualifier in principle is used because friction in the hour gears causes some motion to be transmitted to the minute hand. In daylight saving time the clock must be advanced one hour. Since the hour hand is accessible from the front, it is advanced (clockwise) one turn plus one hour from the original hour. Surprise! The hand returns to its equilibrium position at the original hour minus one hour. Therefore, to advance one hour, turn the hour BH one turn counterclockwise. This article analyzed and compared two clocks that used one movement clock and at least one balanced hand. The one-movement-balanced-hands clock described in this article is covered by the U.S. patent 7,683,381, One Movement Balanced Hands Clock, issued on January 5, 2010, by Rubens A. Sigelmann Ward Francillon Time Symposium at the Crowne Plaza Williamsburg at Fort Magruder adjacent to Williamsburg, VA Topic: Conservation, Restoration, and Repair Lectures, Workshops, Special Tour: Colonial Williamsburg Museums See August MART or nawcc.org for registration form and additional information. October 28-30, 2010 Sponsored by Old Dominion Chapter August 2010 NAWCC Watch & Clock Bulletin