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Introduction The aim of this report is to evaluate various methods used in the analysis of mechanisms, with the intension of employing the use of the most suitable method within the company. The primary requirement is to cut production cost by reducing the amount of work sub-contacted to other companies. To this end the chosen method of analysis will be used by the design engineers of the company to complete calculations regarding velocity, acceleration and force analysis for the mechanisms. The chosen analytical method should therefore meet the following requirements: The methods that will be evaluated in this report are: In order to effectively evaluate each method for analyzing mechanisms a simple four bar mechanism has been chosen, shown in Figure 1.1.

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For each method a detailed analysis will be done of the mechanism and the results compared from the other methods. Analytical Method The analytical analysis of the mechanism shown in Figure 1.1 is divided into 2 separate four bar linkages. The first 4 bar linkage can be seen in Figure 2.1, the complex exponential vector loop equation for the linkage can be written out, this can then be expanded using the Euler expansion and separated into real and imaginary parts to get simultaneous equations. The simultaneous equations can then be solved to determine the unknowns. The full derivation of these equations can be found in the following text, R.L.NORTON, Design of Machinery, 1st Edition: Position analysis - Ch 5, p176-177 The resulting quadratic equations found by solving the simultaneous equations indicate whether the linkage is in its 'open' or 'closed' (crossed) configuration, this is indicated by real and distinct quadratic roots.

It also indicates if the mechanism is bordering on stability of two configurations, that is the mechanism is able change from open to closed configuration whilst running, this is indicated by the quadratic roots being real and repeated. Lastly if the quadratic roots are complex conjugates then the mechanism is said to be non-Grashof.

The Grashof condition is a simple relationship that predicts the rotation behavior of a mechanism, non-Grashof is where 'no link is capable of making a full revolution with respect to the ground plane'. The second four bar linkage can be seen in Figure 2.2. The complex exponential vector loop equation is then derived, and using the same process as the first four bar linkage, two simultaneous equations are developed for the two unknown values, the angle of the link DP, and the sliding link length of link CA.

Below is a summary of the five equations used in the spreadsheet analysis of the second four bar linkage. A full derivation of the 2 nd four bar linkage can be found in R.L.NORTON, ' Design of Machinery', 1 st Edition, sections 4.7 - Position, 6.7 - Velocity & 7.3 - Acceleration. Equation 2.4 - Euler Identity The Euler Identity is used when a complex vector equation exists, since is splits the equation into it's real and imaginary parts. Detskie risunki na temu moya rodina kazahstan youtube. This is known as Euler Expansion.