This application is used to calculate designs for various types of gears, and to render their outlines. It can be used to prepare SVG files for export to CAD tools or CNC machines, or can just save images of gears as JPEG files. The gear calculator is a command line/shell script application, that uses the command line for input, and either the standard output or a text file for computed results.

The application is also made available as a small web application, implemented using Blazor web interface technology. Everything that can be done from the command line is available, and more easily accessed, from the web app when launched.

The command line application is invoked as follows:

gears [primary-option] [option-specific-arguments]

Every command has one primary option, followed by multiple additional arguments. The arguments that follow the primary option depend in type and number on which primary option has been selected.

The following table describes what each primary option will do for you

Regardless of which primary option has been selected, there are a number of follow-on options that are applied to many different gear types being generated.

Each option has a short form with a hyphen and a single letter, or a longer form beginning with two hyphens. For example, --profileshift 6 and -ps 6 perform the same task, setting the desired profile shift of the gear to 6%. What follows is a chart of the common options to be set for various types of output gear:

In the middle of a gear it is possbile to cut out spokes, a central spindle hole for the axle to be inserted, and even an inlay for a ball bearing and/or a keyed cutout to lock adjacent teeth together. The options to configure these can be set for all gear types. The application will use its own algorithm to decide whether the gear is big enough to warrant creating spokes, but the other spindle options are all available to you to set:

In addition to the common and cut out options described above, each gear type has specific options that apply only to gears of that type. For involute gears, these options are listed below.

An example of a command line for building an involute gear might be as follows:

gears involute -t 18 -a 0.01 -m 5 -c 3.18 -s 6 -pa 14.5

This creates two files - a JPEG file and an SVG file for the same gear. The gear has 18 teeth, with a module of 5mm. It is designed to be cut out with a 3.18mm diameter end mill or smaller. It has a spindle hole diameter of 6mm and the teeth always make contact at 14.5 degrees to the tangent passing through the contact point. Finally by setting the plotting accuracy to the nearest 0.01 mm, the number of points in the plot is kept low.

Default values are used for the missing parameters. There is zero backlash (unwise, as machining errors may lead to friction), zero profile shift where the gears are moved closer together or further apart and the tooth shapes adjusted accordingly, and no bearing inlay or hexagonal keying.

A unique filename for each of the output files is created, based on the parameter values passed on the command line.

The set of arguments speialised for a clock chain are given below. Note that when we use the term 'clock chain', we mean a chain made of circular wire loops folded into rings that are interleaved with each other. In other words, a classic chain as might be used for a barrier or indeed to hang clock weights.

In clock making, involute gears have historically not been used very much. Traditionally gears based on epicycloids and their mating hypocycloids would have been used. These have the advantage that machining the hypocycloids can be made extremely easy, but the disadvantage is that the gears are very sensitive to separation distance between the gear centres. One valuable benefit is that gears with very small numbers of teeth can be designed without those gears binding or being weakened by undercutting. This is useful for high gearing ratios.

Some notes on these options might be helpful. The full height of the cycloid tooth is the distance radially from the pitch circle out to the point at which the rising epicycloid crosses the falling epicycloid for the back of the tooth, i.e. the middle of the tooth. We blunt the tooth so that the dedendum of the tooth opposite is reduced, meaning we don't have long thin teeth that could be quite weak. The downside is that the contact ratio (the average number of teeth in contact between the two gears) reduces. We never want the contact ratio to drop below unity as that would mean there are times in which no two teeth are in contact.

There is another benefit too. Involute gears have a constant pressure angle between the teeth throughout their contact time. Cycloidal gears have a pressure angle that starts quite severe near the ends of the teeth but passes through zero when the contact point lies on a line between the two gear centres. By blunting the teeth, we are able to remove some of the contact time that occurs at severe angles thus reducing the maximum pressure angle.

Clock movements have special wheels that often have sharp angular teeth used to drive the pallets attached to the top of a pendulum. As the pendulum mechanism is known as the escapement, these wheels are known as espace wheels.

Escape wheels are characterised by having a flat face on the leading edge of each tooth, a tooth tip width for strength, and a sloping rear to each tooth to maintain the tooth strength. Between each tooth at its dedendum there is an arc that joins the back of one tooth the the face of the next tooth. The effect is to create a tooth that looks like a circular saw blade. To see some examples of this, try experimenting with the options in the table below:

A ratchet when combined with a ratchet pawl allows a wheel to turn in one direction but prevents rotation in the opposite direction. These are often used for winding mechanisms such as lifting weights. Ratchets are actually similar in design to escape wheels, except there is a gradually rising curve from the base of one tooth to the tip of the next. The drop from a tooth tip to the base should be abrupt so that there is no chance of a pawl bouncing up and allowing the wheel to slip backwards.

Sprockets for clock chains are much less common that the sprockets we are all familiar with for roller chains. An obvious example of this is the classic bike chain with its characteristic bike gear sprockets. This gear type is used when designing a sprocket for a roller chain of this type.

The reason we need the chain width is because the designed sprocket can allow the edges of the chain to lie on a circular base to either side if the sprocket teeth if desired.

gears -m [numerator] [denominator] [min-teeth] [max-teeth]

Sometimes we need to map a gear ratio back onto the same axle using two gear pairs. For example, this happens in a clock movement where the hour hand must rotate at one twelfth the rate of the minute hand, but is coaxial with it. Two gears are used to achieve the 1/12th reduction, using the two gear ratios 1/4 and 1/3 for example. This option allows you to find the number of teeth on both the gear and the pinion for the two gears so that they have the same axle separations, for any overall gear ratio of numerator/denominator.

Example: gears -m 1 60 10 96

This would search for all combinations of pinion and gear tooth counts for pairs of gears that together have the same axle separation, but that also give an overall ratio of 1/60th. No tooth or pinion will have fewer than 10 teeth, nor more than 92 teeth.

gears -C [output-file-path]

Creates a table of data for a range of gears with various pressure angles, tooth counts, and profile shifts. The results are written to the file given in the output file path. For each tooth it tabulates the following data:

Following this list, a table appears that shows for each pair of gears cut to this profile-shift and pressure angle, what the contact ratio is between two gears with their respective numbers of teeth. All combinations of tooth pairs from the range 10, 12, 14, 16, 18, 24, 30, 36, 48, 72, 144 are plotted.

The contact ratio is defined as the average number of teeth that are in contact on the involute part of their gear surfaces at any one time. If less than 1, the gear tips will be grinding on the undercut parts for some of their rotation, and will run unevenly and noisily. Ideally this ratio should be above about 1.1 for smooth handover between teeth.

gears -c [pressure-angle] [teeth1,teeth2 ... teethM] [module] [profile-shift1] [profile-shift2] [cutter-diameter] [output-filename]

Creates a table of data for the gears whose pressure angle and comma-separated list of tooth counts have been specified in the arguments. The comma-separated arguments must not have any embedded spaces.

Table data is as for the -C option described above, but with a single selected pressure angle, a seleted list of tooth counts, a module, and cutter diameter. Two profile shifts are provided so that the contact ratios between pairs of gears each with a different profile shift can be listed. The pressure angle is specified in tenths of a degree, the profile shifts are percentages of the module, and the module and cutter diameter in 100ths of a mm.

For the -C option, we assume a sufficiently small diameter cutter so that the undercut and dedendum do not need to be adjusted from the ideal curve. Also for the -C option, we assume the module is 1.0mm as a working default.

Example: gears -c geardata.txt 145 10,12,15,45,48,50 500 21 -21 635 output.txt

Computes the tables for the 14.5 degree pressure angle, for all gear tooth counts in the list of values supplied as the second parameter. The gears have a module of 5mm, and are cut using an end mill of diameter 1/4 inch (6.35mm). Given a profile shift of 21% and -21%, all contact ratios between every pair of gears specified in the list of tooth counts for profile shifts either way round are listed. The results are written to the file output.txt.

This product is published under the standard MIT License. The specific wording for this license is as follows:

Copyright 2020 Ropley Information Technology Ltd. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

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