Special gear ratios for astronomical purposes

Introduction

When facing the task of building a gear train with a reduction ratio unobtainable with standard gears, the problem can be solved by using a differential. The differential splits the desired reduction ratio in 2 terms, both of which may be achieved by means of availbale spur gears.

An 1:365 ratio can be used in astronomical clocks as the ratio stands for 1 day : 365 days or 1 day : 1 year.

Bert Love wrote an article in the februari 1970 Meccano Magazine about the usage of the 73t sprocket in combination with a fork piece to achieve a ratio of 1:73. In combination with a 19t/95t gearpair a 1:365 ratio could be achieved.

Recently I came across another clever approach by Ariel Verlatsky, based on non standard gears and by engaging a gear wheel with a sprocket by a chain. Based on his idea I created a version which stays a bit closer to the Meccano standard gears. It still uses the 73t sprocket.

To obtain a 1:365 ratio with gears only - and this is in my opinion by far the most elegant solution - can be achieved by means of a differential:

73 = 292/4 = 288/4 + 4/4 = ½ x (288/2 + 4/2) (the YouTube video mistakenly mentions 4 in the denominator…a typical fingerfast brainslow moment…)

73 = ½ x (288/2 + 4/2) = ½ x (ratio satellite left + ratio satellite right)

Number 288 can be divided in 2 x 3 x 3 x 4 x 4 or in a ratio of : 50:25 x 57:19 x 57:19 x 60:15 x 60:15. Number 4 can be represented as a ratio of 60:15. See further the vid.

The knowledge about differential equations was taken from a FAC system manual from 1959. As far as I know this solution has never been described in Meccano Magazine or any other Meccano related magazine.

1:365 ratio to define the relation between a day and a year

Designing an 1:365.25 ratio

An interesting addition to the previous assembly could be an extra differential to define the sidereal time as shown in the picture below. Compared to the light blue axle, the dark blue axle rotates 365.25 times. Multiplied by 4 this axle gives a difference of 1 day (366 days ) for every 4 years. This output could be part of a mechanism to define a leap year.

1:365.25 ratio to define a leap year