Mechanical Design Handbook

Chain drives are used to transmit rotational motion and torque from one shaft to another, smoothly, quietly and inexpensively. Chain drives provide the flexibility of a belt drive with the positive engagement like a gear drive. Therefore, the chain drives are suitable for applications with large distances between shafts, slow speed and high torque. Usually, chain is an economical part of power transmission machines for low speeds and large loads. However, it is also possible to use chain in high-speed conditions like automobile engine camshaft drives. This is accomplished by devising a method of operation and lubrication. Compare to other forms of power transmission, chain drives have the following advantages: Chain drives have  flexible shaft center distance, whereas gear drives are restricted. The greater the shaft center distance, the more practical the use of chain and belt, rather than gears. Chain can accommodate long shaft-center distances (less than 4 m), and is more...

In this post, you'll find the video clip to show how to use the excel program to solve system of equations using Gauss Elimination method and download link. You can find the links related to this series of post below: Solving System of Equations using Gauss Elimination Method (Part 1) Solving System of Equations using Gauss Elimination Method (Part 2)   Solving System of Equations using Gauss Elimination Method (Part 3)   Solving System of Equations using Gauss Elimination Method (Part 4)   Solving System of Equations using Gauss Elimination Method (Part 5)   Free download excel file of equations solver with Gauss elimination method You'll need the following password to unzip: mechanical-design-handbook.blogspot.com

Let's continue from [ Solving System of Equations using Gauss Elimination Method (Part 4) ]. Now you know how to enter data and solve a set of linear equations using our program. Now it's time to see how to setup another set of equations. Let's try to solve system of equations with 10 unknowns. From the following screen, click "Main Menu". Program will move to main screen with pop-up windows. Enter number of equations to be solved, for this example, enter 10 and click OK. Warning screen will appear as follows. Please note that the program allows to keep only 1 set of equations at a time. Existing equations will be deleted we you set new equations. If you wish to solve new set of equations, click "Yes". Program will move back to the calculation screen. You'll find matrix [A] with 10x10 dimensions, vector {B} with 10x1 dimensions and vector {X} with 10x1 dimensions. The program erased all existing data and create new table automaticall...

After you download an excel program Gauss Elimination Method from our web site and open it, you'll find the following screen. You have to click "Options..." and "Enable this content" to enable the VBA otherwise the VBA code will be blocked and can't run the program. The program will show a form asking for your agreement confirmation. After you've agreed, you'll find the main screen, then click Start. You'll find the menu whether you need to review or recalculate the previous equations or you want to add new equations. Let's try review the earlier equations by clicking at "Existing equations" button. The program will move to another screen where you can change values in matrix [A] or vector {B} and recalculation to solve the equations with the same number of equations. For this example, the dimension of matrix [A] is 3x3. So if you want to solve another set of linear equations with 3 unknowns then you can modif...

From post [ Solving System of Equations using Gauss Elimination Method (Part 2) ], we know the procedures of Gauss Elimination method to solve system of linear equations. But if we write excel VBA program based on those procedures, we may encounter with problems and cannot get the calculation result. You can find more details regarding problems and how to correct them from [ Numerical methods in engineering ]. We will explain one problem that may occur. It's division by zero. For example, we want to solve a set of simultaneous equations as follows using Gauss Elimination method. The first step of Gauss Elimination method is to divide equation (1) with a coefficient of x 1 which is 5. This is fine to do that. But imagine if the equation (3) and (1) are swapped as follows, we will encounter with "division by zero" problem. Actually we will have problem if the value in diagonal term of matrix [A] is zero or has very small value. So we can avoid this problem by swa...

The the previous post [ Solving System of Equations using Gauss Elimination Method (Part 1) ], the basic information regarding Gauss Elimination Method has been shared. In this post, we will have at more details about Gauss Elimination method . Why called "elimination"? The general form of system of equations is like this. The Gauss Elimination method starts from forward elimination by dividing equation (1) with coefficient of x 1 . Equation (1) now becomes: Multiply equation (1) with coefficient of x 1 from equation (2) then we get: Then we subtract equation (2) with equation (1). Equation (2) becomes: Or we can write it as Repeat the same procedures for the remaining equations and we get the system of equations as follows: We can see that the first term in equation (2) to (n) are eliminated for this round of calculation. For the next round, we will repeat the same procedure, only we change the coefficient to equation (2) i.e. dividing equation (2) w...

Sometimes engineers need to solve a system of equations to obtain solutions for their engineering design works. This kind of problems consists of several number of unknowns and equations that cannot be solved easily without good knowledge of system of equations solving method and understanding of computer programming. If we need to solve a set of linear equations with 2 - 3 unknowns, it will be easily to solve by hand calculation. There are several methods available for solving them. But when we need to solve much more unknowns e.g. 20 unknowns or 1,000 unknowns, computer software is unavoidable. System of equations with "n" linear equations can be expressed as follows: We can write it the matrix form as [A]{X} = {B} The dimension of matrix [A] is (nxn), vector {X} is (nx1) and vector {B} is (nx1). There are several methods to solve a set of simultaneous equations e.g. Cramer's rule , Gauss elimination or Gaussian Elimination method , Gauss-Jordon method , matr...

The Peaucellier–Lipkin linkage (or Peaucellier–Lipkin cell), invented in 1864, was the first planar linkage capable of transforming rotary motion into perfect straight-line motion , and vice versa. It is named after Charles-Nicolas Peaucellier, a French army officer, and Yom Tov Lipman Lipkin, a Lithuanian Jew and son of the famed Rabbi Israel Salanter. Until this invention, no planar method existed of producing straight motion without reference guideways, making the linkage especially important as a machine component and for manufacturing. In particular, a piston head needs to keep a good seal with the shaft in order to retain the driving (or driven) medium. The Peaucellier linkage was important in the development of the steam engine. The mathematics of the Peaucellier–Lipkin linkage is directly related to the inversion of a circle . There is an earlier straight-line mechanism, whose history is not well known, called " Sarrus linkage" . This linkage predates ...

The Hoekens linkage is a four-bar mechanism that converts rotational motion to approximate straight-line motion. The Hoekens linkage is a cognate linkage of the Chebyshev linkage . " DESIGN OF MACHINERY " by Robert L. Norton shows the link ratios that give the smallest possible structural error in either position or velocity over values of Δβ from 20° to 180°. The followings are some interesting examples of Hoekens straight-line mechanism from youtube. Walking robot Marble machine Source: http://www.designofmachinery.com/DOM/Chap_03_3ed_p134.pdf http://en.wikipedia.org/wiki/Hoekens_linkage http://www.youtube.com/watch?v=AkI1nrq9mMQ http://www.youtube.com/watch?v=-CKgP_cueEw http://www.youtube.com/watch?v=PxpRUpmRdCY