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Showing posts from November, 2009

### 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.

### Timing Diagram (Part 4 - Timing Diagrams Comparison using Motion Simulation in Microsoft Excel)

In post [Timing Diagram (Part 1 - No Overlap Movement)], we saw the design requirement that we have to design the die to work together with the indexing mill with the construction as shown below.
Without detailed calculation, we could end up with a very simple timing diagram as shown below.
But it's not good enough. The die has to wait for the indexing to finish its movement before moving. This reduces the indexing time of the die, and get high acceleration on the die.

In post [Timing Diagram (Part 2 - Maximum acceleration calculation)], we calculated the maximum acceleration of Cycloidal motion cam profile and saw the opportunity to reduce the acceleration by extending the indexing time.

In post [Timing Diagram (Part 3 - Cycloid Cam Profile Analysis)], we analyzed the cycloid cam profile and see opportunity of overlap motion. Some calculations have been made and we end up with new timing diagram which is smarter than the original one as shown below.

We calculated the maximum acce…

### Timing Diagram (Part 3 - Cycloid Cam Profile Analysis)

In previous post [Timing Diagram (Part 2 - Maximum acceleration calculation)], we calculated the maximum acceleration of the die using cycloid cam profile. We found out that this maximum acceleration of the die can be reduced if we can extend the indexing angle (Bm) or indexing time (tm) through overlap motion.

Then, let's see how we can calculate for the suitable indexing angle to reduce the acceleration of the die.

Cycloidal motion cam profile has movement equation as follows.
h = hm x [t/tm - 1/(2 x pi) x sin(2 x pi x t/tm)]

Rearrange the equation to get
h/hm = t/tm - 1/(2 x pi) x sin(2 x pi x t/tm)

The displacement profile can be plotted as shown below (dimensionless).
We can see that at the first 10% of indexing time, the movement is just only 0.65% of the total movement (stroke) and at 90% of time, the remaining movement for the die is only 0.65% of the total movement (stroke). Or we can say that, there is not much movement at the first and last 10% of indexing time.

For thi…

### Timing Diagram (Part 2 - Maximum acceleration calculation)

Let's calculate the acceleration of the die from previous post [Timing Diagram (Part 1 - No Overlap Movement)]

The die moves using Cycloid cam profile. So first we have to get the formula to calculate the maximum acceleration of cycloid cam profile.

If the machine speed is N (pcs/h) and the indexing angle (degree) is Bm, the indexing time (second) tm can be calculated as follows.

Cycle time (sec) = 3600/N
Indexing time tm (sec) = (Bm/360) x Cycle time = (Bm/360) x (3600/N)

Hence,
Indexing time tm (sec) = 10Bm/N
Cycloid cam profile has the equation of displacement as follows.

h = hm x [t/tm - 1/(2 x pi) x sin(2 x pi x t/tm)]
where:
hm: Maximum displacement (m)
tm: Indexing time (s)
pi: 3.141592654

We can get velocity equation by differentiation.

v = dh/dt = hm x [1/tm - (2 x pi)/(2 x pi x tm) x cos(2 x pi x t/tm)]
v = hm/tm x [1 - cos(2 x pi x t/tm)]
Then, the acceleration is as follows.
a = d2h/dt2 = dv/dt = hm/tm x [0 - (-2 x pi/tm) x sin(2 x pi x t/tm)]
a = 2 x pi x hm/tm2 x sin(2…

### Timing Diagram (Part 1 - No Overlap Movement)

When I search in Google for "timing diagram", I found a lot of results about electrical timing diagram software but they're not about what I'm going to tell. Timing Diagram in my meaning is a tool that represents the sequences of movement of mechanisms. It is a very useful diagram for mechanical design engineers to understand how each part of the machine works together.
" By properly design the timing diagram, we can make machine moves smoother even at higher speed."
We often draw the timing diagram using cam angle (in degree) in horizontal axis and use the movement of mechanism (in mm) in vertical axis.

From the timing diagram, we can find the opportunity to reduce the acceleration (force) of the moving parts so as to reduce the wear in machine.

Experience shows that a lot of mechanisms have been designed without using "overlap" movement. This makes the machine parts move from one point to another point in short period. But if we provide the overla…

### Standards of limits and fits for mating parts (Part 2)

In the previous post (Standards of limits and fits for mating parts), we talked about the definitions of each term related to limits and fits as well as the formulas to determine the values of tolerances. In this post, we're going to convert those information into the real calculation using Microsoft Excel (as usual). As stated earlier, the calculation results may be different from the real values used in general mechanical design handbook. So please use this just for educational purpose only, but use the real table from general limits and fits table if you want to get higher accuracy values.

This is the screen shot of excel file to calculate upper deviation and lower deviation according to the selected shaft diameter and tolerance grade.

Let's see how to manually calculate the deviation values before using the program.

Example: To calculate the upper deviation and lower deviation of a shaft with diameter of 40 mm and tolerance g6.

Please refer to previous post (Standards of li…