A straight line motion is a common application in engineering design and manufacture. The Peaucellier mechanism generates exact straight lines, meeting . The Peaucellier–Lipkin linkage invented in , was the first true planar straight line .. Print/export. Create a book · Download as PDF · Printable version. Peaucellier mechanism is one of the exact straight line motion mechanism working on lower pair linkages implying eight links rhomboidal system in such a way.
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PDF | Straight-line motion, albeit simple, manifest itself in numerous applications, length constraints, the Peaucellier mechanism is one that. Featured an eight-link rhomboidal system with converts pure rotational motion into pure linear motion with length constraints, the Peaucellier mechanism is one . Figure SOLIDWORKS MODEL OF PEAUCELLIER'S LINKAGE. The four-bar linkage can not achieve a perfect straight-line motion. If we want to describe a.
Abstract abstract Straight-line motion, albeit simple, manifest itself in numerous applications, from running steam engines and oil wells to manufacturing parts with straight edges and sides. The drive to maximize production creates a need for continuously running assembly-line manufacturing comprised of precise, individually optimized components. While there are many so-called straight-line generating mechanisms, few actually produce a true straight-line, most generate only approximate straight-line. Featured an eight-link rhomboidal system with length constraints, the Peaucellier mechanism is one that actually produces a true straight line intrinsically. This paper presents a study on the dimension synthesis of the Peaucellier mechanism, namely by identifying the correct ratio of linkage lengths to produce the longest straight line stroke. In addition to designing for stroke, another objective of interest is to attain a desired velocity profile along the path.
As can be visualized from Figures 2 and 3 by rotating In an effort to characterize the factors that optimizes the link O2R, the limit positions occur when the rhombus strokes, a hypothesis was adopted in that the entire rhomboidal collapses both above and below the horizontal.
In following equation. If b were less than this value, the rhomboid would following Figure 4 : collapse perpendicular to rotation before the horizontal position, thus ending the rotation.
However, It did, however, increase the stroke length by allowing the this third configuration can still possibly be used. See below.
In holding c constant while varying a in separate iterations, it was clear that the motion did indeed change. Figure 7 clearly displays that vertical position changes for every input angle and a-value.
The smaller a-values maintain a constant velocity for a longer period of time, but the greater angles they reach correspond to a much sharper acceleration towards the maximum stroke.
Since the purpose of this analysis is to optimize the maximum line length change in y in relation to After the above observations were obtained, the inferred the linkages, a can be held at 1 while varying the other two optimal condition based on the hypothesis that maximum linkage lengths.
In fact, the stroke was consistently greater in the third vertical height at a specific angle at all, Figure 6. It was then noted that a direct evaluation of the stroke function, given by Eq.
Although specifics are 2 indiscernible, it is clear that there is a definite beginning, end, 1 0 and maximum to the relationship between b and c; the 0 50 mechanism can be optimized with proper constraints. Although maximum stroke for a particular c-value, along with the a larger a-value allows a much greater range of b- and c- corresponding b-value as shown in Figure 9.
Note the maximum stroke does not vary significantly. Velocity similarity between the graphs. And the linear correlations analysis will now be employed to create the additional between the maximum stroke Smax and the c values can also be constraints necessary for the design of this mechanism.
In this section, a method is developed to facilitate the Because different values of a merely change x, for any given a dimension synthesis of the Peaucellier mechanism based on value the influence of b and c variables are essentially practical functional specifications, such as stroke, motion interchangeable with respect to Smax.
Therefore, a constant speed is highly desirable. Max Stroke vary c Although the Peaucellier mechanism, along with most other b-value at max straight-line mechanisms, has an output stroke of continuously changing velocity, it is possible to create a near constant range 50 of velocities . The velocity at a specific location can be 0 derived by differentiating the y-value function using either 0 20 40 60 80 method, with the alternate being used as verification.
It is exactly variation.
That is, Equation 15 can then be used to 15 calculate b2-c2 as 1. Figure 10 displays the plot and data table of this equation. This makes sense because can be found.
Although the original analysis proved that the mechanism could not be physically connected if this was larger b and c values cause a proliferation of the stroke length, not true.
The feasible design solutions lie on the hyperbola this application is not practical with the correspondingly above the linear assembly constraint line. One way to provide such 0.
Using equations 8 and 10 for y-value at a Figure Example case 1 solution specific angle and total stroke respectively, the required maximum stroke is related to the working stroke and workable As can be seen above, b and c would need to be much greater angle by: than a at.
Steps that can be taken to avoid this disparity include reducing the 16 difference between the ground link a and the working stroke and increasing the acceptable velocity variation. Based on Case 2. With a Z ratio of 0. Norton, Design of Machinery, 4th ed. The point A of the rhombus is connect to fixed point O2 through the link 2.
The length of the link 2 is equal to the distance between points O2 and O4. By the constraints of the geometry point A moves in a circular path and as the point A moves in a circle point P traverses an exact straight line path normal to the line joining O2 and O4. From the construction of the Peaucellier linkage it is clear that this is a much more complex mechanism than the mechanisms generating approximate straight lines, which were simple four bar linkages.
This mechanism has eight members and six joints. Scott-Russell Exact Straight Line Mechanism The complexity of the mechanisms to generate exact straight lines can be reduced by introduction of one or more slider crank linkages.
It is possible to generate an exact straight line using the slider crank mechanism but the range of motion is limited. One such example is Scott-Russell Mechanism as shown in the figure. Based on the geometry of the linkage the output motion is a simple sine function of the drive link or a simple harmonic motion. It is evident from the figure that this mechanism is made up of isosceles triangles, AB, AC and AO2 are of equal lengths.