Mechanical Systems 1 Blog

Chapter 6: Velocity Analysis Velocity  - Its more than speed!     Velocity analysis is a crucial part in characterizing a mechanism's motion. Velocity analysis can be used to determine any point on a linkage. This is done by differentiating the position vector of a vector that points from an origin of a coordinate system to the point that velocity is desired.  Figure 1. A point on a crank that velocity analysis is performed on. Velocity analysis on this crank would begin with position analysis, where the position vector would be written as Rpa = pe^(j θ) . Differentiation of the position vector involves pulling out an omega and an imaginary term, in which it would be rewritten as Vpa = pwje^(j θ) . To get the x and y components of the velocity vector, the Euler identity is substituted into the velocity vector. For the figure above, this is written as Vpa = pw(-sin θ  +j cos θ)  . The presence of the j term causes the sine and cosine terms to swap in the vel...

   Chapter Four - Vector Loops Learning to Love Loops!          Have you ever woken up in the morning and wanted to draw a vector loop for a four-bar linkage?                   I haven't either, but we're going to do one today.     Sometimes it is necessary to draw a vector loop for a four-bar linkage. Such a case is with a crank slider, where the rocker is not a physical link and must be imagined. Slider cranks are popular inversions of the four-bar and have real world applications with things such as pistons.          This image depicts a as the crank, b as the coupler, c as the rocker, and d as the ground.     The x and y components of this crank slider can be broken up into two separate equations, as follows:                                 ...

Straight Line Linkages Getting Handy  with Hoeken !     The Hoeken straight line linkage produces approximately straight motion along a curve. This motion can be optimized for straightness or for constant velocity. At the extremes of the two, some sacrifices have to be made. Ov eroptimized straightness and velocity comes at a limited range of motion that this straightness will be in - i.e., the motion will be s traight for a smaller distance. This can be seen by using the table located in the textbook.     The Maximum  ΔCy% column of the table indicates how much Cy is allowed to change along the straight portion of the motion. 0.00001% indicates that Cy can only change in vertical position by that percent - making it the most constrictive option in the table.  Δx in the table is the section of the curve that is straight.      Considering first a  ΔCy of 0.00001% and a L2 length of 1 in, the  Δx value would be 0.601 inches. For ...

  An interesting topic of this chapter is that of fourbars. These mechanisms can be seen in such real-world examples as locking pliers, bicycles, pistons, and oil well pumps. Fourbar mechanisms have three different inversions, meaning that there are three possible links that could be converted into the ground. This produces three other fourbars with unique motion. These are the crank and lever mechanism, double crank mechanism, and the double lever mechanism. Crank and Lever This inversion uses a crank attached to a coupler to drive a lever - as seen in oil well pumps. The lever is able to oscillate about a fixed point in its center where it is attached to ground. Due to the rotation of the crank, a piston or other attachment is able to produce a repeating motion. Double Crank  This mechanism has two cranks that are connected by a coupler. This mechanism powers locomotive wheels. The cranks rotate, which rotates the wheels of the locomotive. Double Lever The double-lever mecha...

 An interesting topic of this chapter is that of fourbars. These mechanisms can be seen in such real-world examples as locking pliers, bicycles, pistons, and oil well pumps. Fourbar mechanisms have three different inversions, meaning that there are three possible links that could be converted into the ground. This produces three other fourbars with unique motion. These are the crank and lever mechanism, double crank mechanism, and the double lever mechanism. Crank and Lever This inversion uses a crank attached to a coupler to drive a lever - as seen in oil well pumps. The lever is able to oscillate about a fixed point in its center where it is attached to ground. Due to the rotation of the crank, a piston or other attachment is able to produce a repeating motion. Double Crank  This mechanism has two cranks that are connected by a coupler. This mechanism powers locomotive wheels. The cranks rotate, which rotates the wheels of the locomotive. Double Lever The double-lever mechan...