Weekly Challenge Group

Avoid adding constraints that are not in the statement:

The reason I raise "a generic object" is to avoid adding constraints to the design. If, for the purpose of giving an example, we associate this object with a real one (such as a garage door, seen from its side), for some it could create restrictions that, in reality, are not part of the problem posed (such as imagining the context of the garage and try to avoid collisions with the floor or ceiling, or other things that are not part of the problem statement).

Even the following animation could induce constraints that are not explicitly stated in the statement, since the statement doesn't say anything about what should happen between positions 1, 2, and 3. However, it can be considered a guide indicating that a "smooth transition" between said positions would be desirable.

The garage door example makes me think of just adding two tracks to guide each end of the door. Not very elegant, but it should work

I drew the mechanism showing the 3 positions. Then chose a pivot point at an arbitrary distance from each end of 50. I then connected these pivot points with two simple arcs to define pivot arm lengths. I chose an arbitrary crank arm length of 500 arranged such that at 180 degrees of travel it would drive the object to positions 1 and 3 but no further. To minimize complication of the base, the crank arm pivot was placed exactly below the upper pivot arm hole. This sketch was used as a base to create all the components which were then derived into their own respective part files.

These individual part files were then inserted and constrained in a standard assembly.

Finally 3 assembly model states were created with the object constrained at the 3 different angles. Views were created of those model states and check dimensions were placed.

The design remains completely parametric. Changes to the original layout sketch are automatically propagated through the individual parts and to the assembly.

Of course it works, although it could happen that the route has dead ends that force to change the point from which the system is driven.

This is the classic "analytical solution" that we usually study under the name "synthesis of three positions".

It is very interesting to note that this method provides infinite solutions depending on the two points that one chooses to articulate the system. Some choices cause link crossings and deadlocks that force the actuation point to change. The nice thing about kinematics in the CADD environment is that you "pick a point to drag" the mechanism and eventually you can only reach a certain point on the trajectory and then you are forced to change it (it was not your case).

The figure shows two possible choices of articulation points, which cause different mechanisms and behaviors (even going through the same three positions).

The analytical solution provided by Bob led me, first, to mention the "three-position synthesis" method. He considers that, for any point of the object, we have 3 positions that define an arc of circumference. With which, we can connect said point with the center of that arc through an articulated link. Any two points on the object are sufficient to drive it (using two links) and ensure that it "will pass through the three required positions". The following figure summarizes this analytical consideration:

Second, he allowed me to observe that the choice of these two points is arbitrary, but that some work better than others. Bob's choice does not present movement problems, but if I change only one of the points, I get the other solution that we see in the figure of my previous post (which cannot be dragged continuously through the entire path).

This comment, in turn, leads to an analysis of what happens with the choice of different points. In the following animation you will see an option almost identical to the one proposed by Bob, which works well, and which allows you to appreciate the other point that was chosen for the solution that does not work well. If we observe this point when it is dragged by the mechanism of solution 1, we will see that it follows a trajectory (shown as a continuous black line) that is different from the one it follows when said point is chosen to drive the mechanism (the arc of circumference in dashed line in solution 2, which doesn't work well).

The first important observation is that "the choice of the two points" is arbitrary and causes the object to pass exactly through the three required positions, but the movement it develops "between these three positions" is not exactly the same (and in some cases , this movement will present deadlocks).

Anyway, it seems like a small and insignificant analysis... but when we try to apply the ideas to a real case, something more complex, the usefulness of a somewhat deeper understanding of this and any other method will become evident, which we should not use robotically but with awareness of the decisions we make.

While the two points were arbitrary, it was possible that my initial selections would have resulted in a deadlock condition. The selection of the two points then becomes mostly a trial and error approach. Generally, the further apart the points, the less chance of a deadlock.

The spacing of the points is a very interesting practical criterion, Bob, and equally affects guide-type solutions, such as those mentioned by @Jack K.

If the real case were a garage door, perhaps we would like to have both articulation points on the same side (as in the solution I showed that doesn't work well).

If we try, we will discover that we go from a situation of opposing arcs (like the one you have proposed) to the opposite situation through a "transition" zone in which the arcs are very large (one of them is an arc centered on infinity... that is, it describes a straight line). These solutions work, but they add a new problem: the pivot point is too far away!!!

But this "new problem" gives us the possibility to discover other interesting things: how can we rotate around such a far point, without making a link really that long?

how can we rotate around such a far point, without making a link really that long?

Instead of rotating, we could slide that point along a straight track

Solutions based on guides are always very interesting and will be one of the options to consider. The other is articulated mechanisms, which may be preferable in very dirty environments because they only have axes that rotate a fraction of a turn (in general). Do you want to try it?

In order not to lose enthusiasm, I leave you with an idea that serves as inspiration for a mechanism capable of replacing a very long link, which describes a smooth arc or, even, a line segment (as a particular case of the arc centered at the infinite).

Could you adjust it, finding out the dimensions it should have to replace a certain long link?

It is interesting to note that the previous mechanism, which can avoid a far center of rotation, and the first one used to move the object are, in reality, variants of the same four-bar mechanism whose connecting link (Biela) can have any shape (represented by a light blue circle). The interior points of this link have varied and very interesting movements for different applications:

For example, it is possible to design a crane that lifts a weight from the ground, passing over any obstacle and deposits it in another area at a higher height. But, being a mechanism with 1 degree of freedom, this complex trajectory is achieved with a single actuator:

SYNCHRONIZED GATES

The next challenge was the one I originally thought to pose. But then it seemed appropriate to take some preliminary steps, by way of introduction, with a simpler generic case that allows us to discover or rediscover simple mechanisms such as the 4-bar.

This real challenge consists of "synchronizing the movement of two gates" that are articulated on a base (in black in the figures). The largest gate (in green) travels a total angle of 90° thanks to a hydraulic drive, not shown, and its movement is intended to lead to that of the smaller gate (in red). This small "conducted gate" covers a total angle of 130° but, in addition, its movement is such that it avoids interference with the "conductive gate". The following animation gives an idea of the movement required, without showing the mechanism capable of achieving this synchronization:

The table in the following figure shows several values of the angle of the driven gate for each value of the angle of the driving gate. Clearly, the relationship between the two is not linear (see graph below) and it can be noted that at the beginning of the movement, from angle 0°, the driven gate moves faster than the conducting one to give it room and avoid interference.

Those who wish to try it can download the files of the following model. It is about 3 figures in DWG format (like the ones I received to solve the problem): both gates and the base.

Synchronized gates (practice on mechanisms) | 3D CAD Model Library | GrabCAD

It is important to give it a personal try, even if it doesn't work or works imperfectly, because it will make it much easier to understand the correct solution when we present it later, to discuss its most relevant details.

A solution with a 4-bar mechanism

The solutions using 4-bar mechanisms are, theoretically, infinite, although similar, since the length adopted for the conductive link can vary in a certain range and conditions the rest of the lengths.

Mechanism fixed link:

Moving links:

Main positions:

Actual implementation:

Knowing "a solution" to the problem implies knowing the "What and How" of the resolution... but that can even be taken from a book or copied from an existing design. The really useful thing is to know the "Why" it works!

Analyzing the latter was the intention of my challenge but, like any learning, it is only possible if it generates some interest.

This was a fun challenge, I never have done something like this before.

I'm glad you liked it and I hope you find it useful in the future. Greetings!

An example of a simple mechanism that combines articulated links and guides for the purpose of controlling the movement of the buckets of a special elevator.

The difficulty lies in the fact that its two straight branches are very close and it is not possible to apply a simple drag chain that, at the same time, controls the rotation of the bucket. I used three guides that control "drag", "rotation" and "variable separation between buckets".

If you want to see more details they are at:

CP-572 | 3D CAD Model Library | GrabCAD