Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.


Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

Chain Drives Design (Part 3)

Let's take a look at the formulas related to chain design.
The pitch diameter of a sprocket with N teeth for a chain with a pitch of p is determined by

Note: the angle of sine function must be degree (not radian)

The center distance, C, is the distance between the center of the driver and the driven sprockets. It's the distance between the two shafts coupled by the chain drive. In typical applications, the center distance should be in the following range:

The chain length, L, is the total length of the chain. Because the chain is comprised of interconnected links, the chain length must be an integral multiple of the pitch.
"It's preferable to have and odd number of teeth on the driving sprocket and an even number of pitches (links) in the chain to avoid a special link"
The chain length is expressed in number of links, or pitches (not in mm or inches!), can be computed as

The center distance for a given chain length can be computed as

Please note that the computed center distance assumes no sag in either the tight or the slack side of the chain, and thus it is the maximum center distance. Negative adjustment and adjustment for wear must be provided.

The angle of contact, θ, is a measure of the angular engagement of the chain on each sprocket. The arc of contact θ1 is for the chain on the smaller sprocket and it should be greater than 120o. It can be computed as


And the angle of contact of the chain on the larger sprocket, θ2, can be computed using

Source:

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