In an earlier video, we explored the concept of Nadi, Vinadi and Prana.
Units of time used in the ancient Hindu calendar or Panchang.
These units are identical to what we are familiar with: Hours, Minutes and Seconds.
I will walk you through the design process for building the clock.
I assume that you have basic knowledge of any CAD software and drawing program.
I have used FreeCAD and Inkscape for the same.
In this video, I will discuss gear ratio calculations. In the next video, we will design gears and the housing for the same.
Let us start by getting familiar with the dial of the clock.
Outer rim has sixty divisions representing 60 Nadi(s) of the day. 1 day equals 23 hours, 56 minutes and 4 seconds approximately. Not to be confused with day and night.
Numbers on the dial in steps of 5 are shown in line with the regular clock.
These divisions are also shared by another unit, Vinadi. One Vinadi is 60th part of Nadi.
Inner circle is divided into 6 parts.
One Vinadi equals six Prana.
Prana is the smallest unit for this clock.
One Prana is approximately 4 seconds. Average time required to breath in and out for a healthy young adult.
We will use four hands for our clock.
This large black hand for Nadi, shining hand for Vinadi,
Green hand to indicate the number of Prana's in Vinandi and small hand for Prana.
This hand will rotate once every 4 seconds to indicate that one Prana is over.
After every rotation of the small hand, the green hand will move 1/6th or 60 degrees on the outer dial.
After six rotations of the small hand, the green hand will complete one rotation indicating one Vinadi is over or 24 seconds approximately.
Long hand will rotate once to indicate completion of one Vinadi.
Gear Ratio calculations
Any spreadsheet application can be used for this activity. I am using Microsoft Excel
This 12V 30 RPM DC motor will drive the whole mechanism instead of a pendulum or winding mechanism.
As per the rating, it completes one rotation in two seconds.
We need a small hand to complete one rotation in 4 seconds. So half reduction is required.
In this spreadsheet, there are four highlighted columns, each for one hand
Initial one will be for the motor.
Pran
Vinadi 6 - This is the large hand which covers six prana in one rotation
Vinadi hand which moves 1 division for every rotation of green hand
And Nadi
We will write down names of the pointers/hands as well
Now let us enter the desired ratios with respect to Prana hand
Green hand will move 1/6th for every rotation of small hand.
Vinadi hand will move 1/60th of the green hand
And Nadi hand will move 1/(60*60) or 1/3600 of the Green hand or 1/60th of the vinadi hand
This row will let us know what is the actual ratio possible with the set of gears we will be working with. Sometimes the exact ratio is hard to achieve.
We will try our best to match the desired numbers.
Direction of rotation for each hand is also important.
All hands must rotate clockwise.
Each column here represents the axle on which gear is hosted. Direction of each gear will alternate when motion is transferred . Anticlockwise to clockwise and again anticlockwise and so on …
We are not using this column right now.
All our four hands are moving in a clockwise direction.
Gear with 20 teeth will be driven by a DC motor. This is our starting point.
Small pointer must complete one rotation in 4 seconds. DC motor gear will complete one rotation in 2 seconds as per the rating.
We need a reduction of 2 here.
Number of teeth for this gear will be 40
Our ratio for this is 0.5. As this is the input gear for our clock, we will not consider this ratio in our overall calculations
We will use compound gears from now on.
If 40 teeth gear is called a large gear , 20 teeth gear will be a smaller one in the compound gear.
This will mesh with another compound gear 30 and 10
For the first Vinadi axle, let us enter 40 teeth.
To calculate the ratio for this axle, we just have to multiply all the intermediate gear ratios.
We can continue the same method and calculate the applicable ratio for the Vinadi pointer.
Desired and actual ratios match perfectly.
Nadi pointer has similar need. 1 60th of vinadi hence we can reuse the same ratios.
We can add the result of vinandi to this product as well to get the final ratio.