### 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 1)

Chain drives are used to transmit rotational motion and torque from one shaft to another, smoothly, quietly and inexpensively. Chain drives provide the flexibility of a belt drive with the positive engagement like a gear drive. Therefore, the chain drives are suitable for applications with large distances between shafts, slow speed and high torque.

Usually, chain is an economical part of power transmission machines for low speeds and large loads. However, it is also possible to use chain in high-speed conditions like automobile engine camshaft drives. This is accomplished by devising a method of operation and lubrication.

Compare to other forms of power transmission, chain drives have the following advantages:
• Chain drives have  flexible shaft center distance, whereas gear drives are restricted. The greater the shaft center distance, the more practical the use of chain and belt, rather than gears. Chain can accommodate long shaft-center distances (less than 4 m), and is more versatile.
• Chain drives require little adjustment, whereas belts require frequent adjustment.
• Chain drives are less expensive than gear drives.
• Chain drives have no slippage, as with belts, and provide a more efficient power transmission.
• Chain drives are more effective at lower speeds than belts.
• Chain drives have lower loads on the shaft bearings because initial tension is not required as with belts.
• Chain drives have longer life service life and do not deteriorate with factors such as heat, oil, or age, as do belts. Sprockets are subject to less wear than gears because sprockets distribute the loading over their many teeth.
• The sprocket diameter for a chain system may be smaller than a belt pulley, while transmitting the same torque.
Points of Notice:
1. Chain has a speed variation, called chordal action, which is caused by the polygonal effect of the sprockets.
2. Chain needs lubrication.
3. Chain wears and elongates.
4. Chain is weak when subjected to loads from the side. It needs proper alignment.
Standardization of chains under the American National Standards Institute (ANSI), the International Standardization Organization (ISO), and the Japanese Industrial Standards (JIS) allow ease of selection.

The followings are some example of chains from British and ISO standard.

BRITISH STANDARD ROLLER CHAINS
BS 228, ISO R606, DIN 8187

ISO Chain no.
The first two digits are related to the chain pitch. See below table.

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