### 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.

### 3-Position Motion Generation Four-Bar Linkage Synthesis using Unigraphics NX4 Sketch

In the real design problem, it will be more practical with 3 specified positions of a line in sequential order than 2-position synthesis. We can use a logical extension of the linkage synthesis technique described in [Four-bar linkage Synthesis using Unigraphics NX4 Sketch] to do the linkage synthesis with 3 positions.

Assume that we have to design the mechanism that move the link AB through 3 positions as shown below. The rectangle represents the limit of link AB, so link AB cannot interfere with the rectangle.

1) Draw link AB in its three design positions A1B1, A2B2, and A3Bas shown above.
2) Draw construction lines from point A1 to A2 and Ato A3

3) Bisect line A1A2 and line A2A3 and extend their perpendicular bisectors until they intersect with each other. Label the intersection O2.
4) Draw line O2A1. It's link 2.
5) Repeat the same for another end of the link. Draw construction lines from point B1 to B2 and Bto B3

6) Bisect line B1B2 and line B2B3 and extend their perpendicular bisectors until they intersect with each other. Label the intersection O4.
7) Draw line O4B1. It's link 4.

8) Draw line O2M and set the same length as O2A1.
9) Draw line O4N and set the same length as O4B1.
10) Draw line MN and set the same length as A1B1.
11) Set angular dimension between O4B1 and O4N to any desired value e.g. 15 degrees.

12) Select "Animate Dimension" Command in Unigraphics NX4 sketch and set lower limt to 0 and Upper limit to 56.355 (or any other value) and Steps/Cycle to 150 (the more steps, the smoother simulation).

See the results of four-bar linkage from three-position motion generation synthesis in the following video clip.