Showing posts from April, 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.

Numerical Methods - The Newton-Raphson Method to Solve Mechanical Design Problems Part I

Machine designers have to deal with several number of equations in their design projects. There are a number of ways to solve for roots of algebraic and transcendental equations. Sometimes, the roots could be obtained by direct methods. However, there are many more that could not. The classical equation such as f(x) = e-x - x cannot be solved analytically. For this case, the only alternative is an approximate solution technique.

There are several methods available to solve the root finding problem such as "bracketing methods" and "Open methods".

The bracketing methods require 2 initial guesses for the root. These guesses must "bracket" the root. The numerical methods using bracketing methods consist of the following techniques:
The Bisection Method: The idea of this technique is incremental search that related to the sign change. Sometimes, this technique is called binary chopping, or Bolzano's method.The False-Position Method: It's the improved tech…

Numerical Methods - First derivative using Excel formula

Numerical methods can be very helpful for calculation of mechanical engineering design. What I would like to introduce in this post is about calculation of the first derivative using numerical methods in Microsoft Excel without using any math software.

From the textbook, there are a lot of formula and explanation about how we get this formula. So I would skip that part and directly start with the selected formula as an example.

We know that the first derivative of function f(x) can be calculated from the following equation

It is the formula to calculate first derivative using interior points that give the error of h4
That means we will use the values of function at other 4 points around the center of interest to calculate the first derivative and the smaller the step size (h), the higher accuracy of calculation result.

The following is the equation of favorite cam curve - Cycloid

The cam follower will slowly move at the beginning of time and start accelerating, then decelerating in the midd…

Design trick about selection of ball joints for fine adjustment of pull rod length

Normally we can find a lot of ball joints with pull rod at every machine. It is used to transmit power from a lever to another link in cam or even pneumatic driven mechanism. It's the part of the system that we can adjust its length due to imperfection in manufacturing of machine parts. For example, we may require high accuracy of mechanism at one position but we cannot achieve it with the fixed length of rod, therefore the use of adjusting rod like this is required.

This adjusting rod consists of right-handed ball joint at one side and left-handed ball joint at another side. This is because we need to adjust the distance between center of both ball joints by turning the pull rod then the screw threads will increase or decrease the distance depending on the turning direction of the pull rod. Of course, if we use right-handed ball joints at both sides, there will be no length changes from turning of the pull rod, but sliding of the pull rod to one side!

Normally, the coarse threade…

Tool Steels

As the designation implies, tool steels serve primarily for making tools used in manufacturing and in the trades for the working and forming of metals, wood, plastics, and other industrial materials. Tools must withstand high specific loads, often concentrated at exposed areas, may have to operate at elevated or rapidly changing temperatures and in continual contact with abrasive types of work materials, and are often subjected to shocks, or may have to perform under other varieties of adverse conditions. Nevertheless, when employed under circumstances that are regarded as normal operating conditions, the tool should not suffer major damage, untimely wear resulting in the dulling of the edges, or be susceptible to detrimental metallurgical changes.

Tools for less demanding uses, such as ordinary handtools, including hammers, chisels, files, mining bits, etc., are often made of standard AISI steels that are not considered as belonging to any of the tool steel categories.

The steel for mo…

Cam Follower Selection

Needle Roller Cam Followers

Needle Roller Cam Followers have a heavy outer ring cross section and a full complement of needle rollers. They offer high dynamic and static load carrying capability, and anti-friction performance, in a compact design. They are used as track rollers, cam followers, and in a wide range of linear motion systems.

Standard Stud cam followers offer the mounting convenience of a threaded stud and are designed to accommodate moderate loads. They are available with and without seals. Standard stud cam followers are also available with crowned outer rings for applications where misalignment is a problem.

Heavy Stud cam followers are designed to provide additional stud strength for applications with
high loading or shock loads. Heavy stud cam followers are available with and without seals, and with crowned outer rings.

Yoke Type cam followers are intended primarily for applications where loading conditions
exceed the capabilities of stud type cam followers, or where cl…