Showing posts from August, 2010

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.

How to use Unigraphics NX4 Motion Simulation in Timing Diagram Design Process - Part 5

The result of timing diagram design using overlapping motion with fifth-degree (3-4-5) polynomial and linear cam functions can be simulated in 3D motion. The simulation is done using Kinematics environment in Unigraphics (UG) NX4 Motion simulation module. The "spreadsheet run" command is used to control the motions of all driving joints as per the timing diagram. Mechanical Design Engineer can then modify and improve the timing diagram before releasing his design for manufacturing.

Here is the NX4 Motion simulation results.

Related articles:
How to use Unigraphics NX4 Motion Simulation in Ti...How to use Unigraphics NX4 Motion Simulation in Ti...How to use Unigraphics NX4 Motion Simulation in Ti...How to use Unigraphics NX4 Motion Simulation in Ti...Further reading related to UG NX
Practical Unigraphics NX Modeling for EngineersNX 6 for DesignersEngineering Design Communication and Modeling Using Unigraphics® NXAdvanced Unigraphics NX2 Modeling and AssembliesParametric Modeling…

How to use Unigraphics NX4 Motion Simulation in Timing Diagram Design Process - Part 4

In [How to use Unigraphics NX4 Motion Simulation in Timing Diagram Design Process - Part 3], we've already set all the links and joints with drivers for links included in Motion Simulation using UG NX4 Motion simulation module. But the driver functions for both indexing mill and punch die are not as per the timing diagram yet. Now it's time to set them according to the timing diagram and see the simulation results in 3D movement.

1. Select "Graphing" command. The graphing command will export the value of displacement of all driving joints (have "driver"). By default, the displacement values of other driven joints will not be exported.

2. Select "Spreadsheet". This is to specify that we need to get the data in excel.
3. Click Ok to confirm.

UG NX4 will then open excel spreadsheet and put the data as shown in the above picture. You can see that the displacement of drv J_Mill and drv J_Die are linear as we specified earlier. Therefore, we will modify…

How to use Unigraphics NX4 Motion Simulation in Timing Diagram Design Process - Part 3

In [How to use Unigraphics NX4 Motion Simulation in Timing Diagram Design Process - Part 2], we've finished setting the driver of revolute joint of the indexing mill. Then let's set the joint for the punch die.

Movement of the punch die is different from the indexing mill. It moves only in linear motion along Z axis (normal to top face of indexing mill). The joint for this kind of movement is called "Slider" joint. Here is how to set it:

1. Select Joint command.
2. Select "Slider" joint icon in the joint dialog box.
3. Select first link icon.
4. Select link "Die" as we previously created

5. Click at the "Orientation on the first link" icon.
6. Select "Point" from the drop-down menu.
7. Select center point of the cylinder as shown above to define the location of the slider joint.

8. Select "Vector" from the drop-down menu to define the direction of the slider joint.
9. Select the bottom face of cylinder to define the v…

How to use Unigraphics NX4 Motion Simulation in Timing Diagram Design Process - Part 2

Let's continue from previous post. Now it's time to see our previous calculation for the timing diagram of indexing mill and punch die in 3D Motion Simulation using Unigraphics (UG) NX4. Though we have made motion simulation in excel spreadsheet using excel VBA, it's much better and easier to do it in UG motion. The UG NX4 Assembly model is prepared as shown below.

Mating conditions of the assembly model is as according to the sketch shown in [Timing Diagram (Part 1 - No Overlap Movement)].

New to UG NX4 Motion Simulation? No problem, just follow our guideline in step-by-step, and you will find it easy to use. Let's see how to do...

We can enter into Motion Simulation Environment as shown below.
In motion simulation environment, we see all commands are disabled. Then we have to right-click on the assembly file and select New Simulation.

This command will create necessary UG files and put them into new folder automatically (see new folder and files in windows explorer)…

How to use Unigraphics NX4 Motion Simulation in Timing Diagram Design Process - Part 1

During the process of timing diagram design, I normally start with some calculations in excel spreadsheet to minimize the acceleration but still satisfy the required process time. I can see the preferred displacement, velocity and acceleration profiles of the mechanisms from excel spreadsheet. What's next? Shall I start manufacturing?

Currently, I use Unigraphics (UG) NX4 to design the mechanical parts. When assembly modeling is done, I normally use the assembly model to simulate the movement of mechanisms with motion simulation module in UG.

It helps confirm the timing diagram before releasing the design for manufacturing. It helps a lot when the movement combined in 3D motion. I can find the interference with another mechanisms and solve it if there is any before release the design for manufacturing.

By the way, when I first start using UG NX4 motion simulation module, I find it easy to set the links and to define related joints for mechanisms. However, I find it difficult to de…

Polynomial Cam Function (Fifth-degree polynomial Example) - Part 4

In the post [Polynomial Cam Function (Fifth-degree polynomial characteristics) - Part 3], we know the characteristics of Fifth-degree polynomial cam profile. In this post we will see the example of using Fifth-degree polynomial together with Linear cam functions to improve the movement of mechanism. We can use the same example as what we did in the post [Timing Diagram (Part 4 - Timing Diagrams Comparison using Motion Simulation in Microsoft Excel)]. The original maximum acceleration of the die for that case without any overlap motion was 4.154 m/s2. But we did the improvement using cycloid cam curve and the maximum acceleration reduced to 0.804 m/s2. That was a big improvement on the acceleration of the mechanism. This time we can find that using Fifth-degree (3-4-5) polynomial cam function can also considerably reduce the maximum acceleration of the mechanism in the same level as cycloid cam profile. But the comparison between cycloid and fifth-degree polynomial for this case is not…

Polynomial Cam Function (Fifth-degree polynomial characteristics) - Part 3

From[Polynomial Cam Function (Derivation of Fifth-degree function) - Part 2], we get the equations for displacement, velocity and acceleration of cam follower using fifth-degree (3-4-5) polynomial. All of these functions can be plotted in Excel spreadsheet as shown in the picture. This is for the case of zero velocity at both ends i.e v0 = 0 and v1 = 0. We can see that it looks like cycloid cam profile which has zero starting and ending velocity. But fifth-degree polynomial has ability to change the starting and ending velocity, while cycloid can't do that. So we have at least 4 parameters to configure the cam curve of fifth-degree polynomial i.e. the total displacement (hm), total angle (bm), starting velocity (v0) and ending velocity (v1). We also have to make sure that the connection between curves must not have any discontinuity. The functions such as cycloid and fifth-degree polynomial has continuity in its displacement, velocity and acceleration. But when connecting it with …

Polynomial Cam Function (Derivation of Fifth-degree function) - Part 2

In [Polynomial Cam Function (Introduction) - Part 1], we discussed about fundamental of cam design and introduction of polynomial cam function. In this post, we’re going to derive the equation of fifth-degree polynomial cam function. We start from the general term of fifth-degree polynomial function as follows.

s = c0 + c1(b/bm) + c2(b/bm)2 + c3(b/bm)3 + c4(b/bm)4 + c5(b/bm)5  ….. (eq.1)
s = displacement (mm)
b = cam angle in that sector (rad)
bm = total angle in that sector (rad)

We can find the velocity in mm/rad by derivative of displacement. Later we can change it to the time domain.

v = ds/db
v = c1/bm + 2c2/bm(b/bm) + 3c3/bm(b/bm)2 + 4c4/bm(b/bm)3 + 5c5/bm(b/bm)4

Rearrange to get,
v = 1/bm[c1 + 2c2(b/bm) + 3c3(b/bm)2 + 4c4(b/bm)3 + 5c5(b/bm)4]  ….. (eq.2)
Acceleration in mm/rad2 can be calculated by a = dv/db
a = 1/bm[2c2/bm + 6c3/bm(b/bm) + 12c4/bm(b/bm)2 + 20c5/bm(b/bm)3]

Rearrange to get,
a = 1/bm2[2c2 + 6c3(b/bm) + 12c4(b/bm)2 + 20c5(b/bm)3]  ….. (eq.3)
Then we set th…