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Polynomial Functions

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  Finding Polynomial Functions  Polynomial functions are versatile types of functions that can be used for cam design. These types of functions can be used for either single or double-dwell.  The general form of polynomial functions are:  In this equation s is the follower displacement, x is the independent variable and the C_n values are the constant coefficients.  The polynomial functions are determined based on how many boundary conditions there are. These boundary conditions are specified on the SVAJ plots. An example of SVAJ plots is shown below.    The boundary conditions that are found are then substituted into the following equations to get the specified constant values to then get the polynomial equation. 

Chapter 6

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  Graphical Velocity Analysis Graphical velocity analysis allows for quick checks of problem to find out what is going on before checking analytically.  In this type of problem you are given a linkage along with w2 and theta 2. With that information you are expected to be able to find theta 3 and theta 4. On the linkage you draw on the velocity vectors perpendicular to each of the links. This allows you to obtain VA, VB and VBA.  You then draw the vectors VA with the correct direction and magnitude. Then you draw in VB and VBA with the correct directions and the intersection point is where the magnitudes are correctly proportioned. 

Chapter 4

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  Sixbar Linkages  Sixbar linkages are linkages that include six links and seven joints. There are two main types of sixbar linkages being Watt's sixbar linkage and Stephenson's sixbar linkage.  Watt's Sixbar Watt's linkage is a type of linkage that combines two fourbars. In this type of linkage the links have parallel motion. The coupler curve that is produced from this gives a straight line. This linkage also only has one degree of freedom. This type of linkage is the simpler sixbar linkage to solve since you can solve it by splitting it into two fourbar problems.  Stephenson's Sixbar Stephenson's linkage is a type of linkage that combines a four bar loop and a five bar loop. This happens because there is two ternary links in the linkage that are combined with a binary link. In this type of linkage there are three unknown angles. This is the more difficult sixbar to solve but it is still possible to be solved using two vector loop equations.  The vector loop e...

Chapter 3

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  Limiting Conditions - What's Stopping You? Chapter 3  It's not you, it's the limiting conditions.  Limiting conditions are conditions that force mechanisms to end up with a specific solution. The limiting conditions allow for a solution for the mechanism to be found rapidly. There are three major types of limiting conditions including: toggle positions, stationary positions, and transmission angle.  Toggle Positions Toggle positions are found by determining the colinearity of links that move within the mechanism. When the coupler and the rocker or the crank and the rocker end up becoming colinear there will be toggle. This toggle position makes the mechanism stuck and will not allow any further motion past the colinear point.  Stationary Positions Stationary positions are locations in the mechanism where there is no movement in it. This can happen when the crank is colinear with the coupler when it is extended or when it is overlapping. This allows for definit...

Chapter 2

The Grashof Condition - As Simple As It Gets The Grashof condition is the condition that must be proven to be true so that one link on a system is able to make a full revolution. This condition is listed as the following:  S + L < P + Q This equation written out is  Shortest Link + Longest Link < Remaining Link 1 + Remaining Link 2 The answer to the equation after plugging in all of the values from your own links will then determine whether or not the linkage is considered to be Grashof. This relationship is one that can make a potentially impossible linkage become much more manageable or at least let you know you need to redo something before moving on. The values on both sides of the equation will help you to understand the motion that will occur.  Classes The values you get on each side of the equation will then allow you to determine what type of class it will be. These classes are to help you determine what inversion of the fourbar linkage it will be. There are...