### 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 Synthesis with Alternate Moving Pivots using Unigraphics NX4 Sketch

In the previous post [3-Position Motion Generation Four-Bar Linkage Synthesis using Unigraphics NX4 Sketch], the locations of fixed pivots O2 and O4 are fixed due to the fixed locations of moving pivots A and B. Sometimes, the location of O2 and O4 are undesirable with respect to your design constraints. More flexible method to get desirable locations of O2 and O4 will be shown in this post.
1) Draw link AB in its three design positions A1B1, A2B2, and A3B3 as shown above.

2) Draw new attachment points C1 and D1 and other lines to form the rigid link ABDC. Do the same for position 2 and 3. Use "Constraint" command in Unigraphics NX4 sketch to set the equal length constraint to all relevant lines e.g. A1C1, A2C2, and A3C3 have the same length, but don't need to specify the fixed value for it. Once we complete these settings at all positions, it means we have set the fixed relationship between our desired line AB and other moving pivots CD.
3) Draw construction lines from point C1 to C2 and C2 to C3
4) Bisect line C1C2 and line C2C2 and extend their perpendicular bisectors until they intersect with each other. Label the intersection O2.
5) Draw line O2C1. It's link 2.
6) Repeat the same for another end of the link. Draw construction lines from point D1 to D2 and D2 to D3

7) Bisect line D1D2 and line D2D3 and extend their perpendicular bisectors until they intersect with each other. Label the intersection O4.
8) Draw line O4D1. It's link 4.

9) Draw line O2M and set the same length as O2C1.
10) Draw line O4N and set the same length as O4D1.
11) Draw line MN and set the same length as C1D1. Do the same for remaining lines, set constraint so that it form the same rigid link as ABDC.
12) Set angular dimension between O4D1 and O4N to any desired value e.g. 20 degrees.

13) Select "Animate Dimension" Command in Unigraphics NX4 sketch and set lower limt to 0 and Upper limit to 60 (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 with alternate moving pivots in the following video clip.