Mechanisms

Among the four videos documenting some methods of converting circular motion to linear or nearly linear motion, I found the model below the most interesting.

http://kmoddl.library.cornell.edu/model.php?m=472&movie=show

I was first attracted to this model above the others because the linear elements were not enclosing the pegs that moved in circular motion.

In this model, the top example shows a rectangular bar positioned above a rotating disk with two raised pegs 180 degrees apart embedded in it. The rectangular bar features two raised pegs of its own towards the left end, and a downward protrusion near its right end. A separate component, shaped at a right angle, hovers its bottom prong over the disk and has the other positioned between the two pegs on the rectangular beam. As the circular disk rotates clockwise, the first peg on it pushes the right angle piece upward, near its tip. This creates torque, rotational movement about the axis at the vertex of the right angle piece. Subsequently, the opposite tip of the piece moves down and to the left. As it is positioned between the two pegs of the bar, it exerts force on the leftmost peg, which causes the rectangular bar to move to the left in a swift movement. The moment after, it loses contact with the right angle piece, and travels toward the downward protrusion that has moved left. When they come into contact, the protrusion experiences a net force down and to the right, but as its motion is limited, moves to the right, again with a swift movement. The cycle repeats when the other peg comes into contact with the right angle piece, and continues.
In the bottom example, a three pointed surface is rotating counterclockwise. It is surrounded by a rounded, irregular hexagonal shape, whose interior features an addition of area to the top left as well as the bottom right. These areas exhibit a right angle facing in the x direction. As a tip of the rotating surface comes into contact with the top right inner face of the hexagon, the hexagon feels a force that moves it to the left. The hexagon has a limited range of movement, in the lateral direction. A small moment after the tip has lost contact with the hexagon on the left side, the tip 120 degrees before it meets the bottom right inner face, which had moved to the left. The face feels a force that directs it to the right, due to its limited lateral movement. The hexagon exhibits a swift movement to the right. The cycle repeats when the next tip comes into contact with the hexagon's inner face.

In both examples, rotational movement is translated into linear, lateral movement of another part. The first example uses an intermediate component, while the second demonstrates that such a part is not required. The greatest difference between the two examples, however, is the number of tips (or pegs) on the rotating component. Both rotational speeds were equivalent. The first example showed two pegs, 180 degrees apart. These caused swift movements of the rectangular bar above from left to right. The second example showed three tips, 120 degrees apart. Because the speed was the same for both, and example two had one more peg/tip, the linear motion changed direction faster for the example with the higher number of tips (more contact because of a greater number of "collisions"). This gave the appearance of a smoother motion of the hexagon as opposed to the rectangular bar. One may see example two as one step closer to a gear than example one, as it has one more protrusion.

This mechanism is useful for translating circular motion into linear motion. I think that the concept demonstrated by the juxtaposition of the two examples can be applied to many things. The smoother linear speed caused by an increase in rotating contact surfaces when angular speed is held constant is helpful for creating less sudden and jerky lateral motion, which would be more functional and ergonomic in examples like bike chains.

I found this mechanism interesting because I was curious as to how the fluidity of motion changes with shape. I wonder how it can change with size and speed.

Well Windlass, Post #4

Reflections

Our design process was as such: we began by brainstorming ideas for the structure of our windlass. Throughout this process, we used our basic knowledge of structures to make educated decisions on the geometries of our components. We then considered physics – force, pressure, torque – to add and modify our components. From the test piece, we used our data to make decisions on dimensions where two components intersected. We then analyzed our testing results to make further modifications to the structure and specific components.

If we had more time, we would definitely return to modifying the handle. We believed that a parallel handle component would ease the cranking of the handle (motion is toward and away, rather than up and down and to the side). However, we made the handle too long (6 cm). The increased torque instead caused the other crank part to begin to rotate about the central rod, disabling it from rotating the winding mechanism. If we had more time, I would definitely try to see if a parallel handle of a shorter length – in combination with a shorter crank part – would eliminate the problem that the larger torque created. We would also try to incorporate the non-essential parts (the hooks and connectors) into our design while also aiming to reduce materials usage.

Accounting

Windlass:

Piece	Quantity	Area of component (cm2)	Total Area (cm2)
Upright	2	115.74	231.48
Disk	2	35.94	71.88
Crank Handle	1	16.71	16.71
Lateral Supports	4	26.26	105.04
Bushings	5	0.71	3.55
Rod (support)	4	5.84	23.36
Rod (central)	1	26.16	26.16

Total Delrin Sheet: 428.66 cm²

Total Delrin Rod: 49.62 cm

Material for nonessential parts

Piece	Quantity	Area of component (cm2)	Total Area (cm2)
Hook	4	22.92	91.68
H connectors	8	3.11	24.88

Total Delrin Sheet of nonessential parts: 116.56 cm²

As we were given 500 cm²  of Delrin sheet and 50 cm of Delrin rod, our stable, functional windlass itself left a remainder of 71.34 cm², and 0.38cm of Delrin rod.

*We cut our rod into the five pieces we needed, so this 0.38cm is used in our structure, distributed over the 5 pieces.

However, we decided to further enhance our windlass by taking on the additional task of keeping it stable on the table surface. If we add the area of the hooks and of the H connectors, then we exceeded our limit by 45.22 cm².

Despite this, we decided to demo our windlass with the non-essential pieces. It worked! 

Well Windlass, Post #3

Testing

When we first tried the windlass, we found that the parallel component of the handle did not contribute positively to our structure. With the length at 6cm, we had hypothesized that the extra torque would make it easier to turn the crank. Instead, we found that the attached crank part began to slip around the Delrin rod and the rod itself showed considerably more strain. Therefore, we eliminated the parallel crank handle.

With this modification, our first iteration windlass worked all three times that we practiced with it. It fully met the dimensional criteria and the expectation that it would not “wobble, shake, or collapse.” However, despite the stability, the Delrin material’s property of low friction worked against us. Although our structure did not wobble or show signs of instability, it slid around the smooth surface of the table slightly when we attempted to use it.

We emailed Professor Banzaert, who told us that we could address the sliding issue if possible. We then decided to see what we could do about this small problem.  

We now came up with hooks that attached to the rectangular parts of the uprights by “H” shaped press-fit connectors. These “L” shaped hooks attached to the base of the uprights and ran perpendicular to the edge of the tables.

The hooks:

   

The "H" connectors:

    

The notches are 0.1875" wide.

With respect to the sketch positions above, two "H" connectors would rotate forward 90 degrees. They would then attach at the very top and very bottom of the leftmost edge of the L shaped hook. The open notches would then affix to the base of one upright

One can see the L hooks and H connectors at the base of the uprights. These components would be supported underneath by the edges of the two tables.

This modification prevented our windlass from moving while we raised the bottle. The windlass still proved to be extremely stable.

Well windlass, Post #2

The Construction period

In the well windlass assignment, we relied upon various methods of fastening and attaching. The method we commonly used was press fitting. Press fitting involves the insertion of a component into an almost congruently-shaped hole to ensure a tight fit and restricted movement. This method was helpful in attaching components of our windlass tightly together to increase strength and stability. We varied the dimensions of the holes to get a better sense of the deviation between the computer dimensions and the laser cut dimensions. In order to ensure the best tightness of the combination, we created a test piece.

Test piece:

The test piece was designed to have circular and rectangular holes of different dimensions so we could best determine the tightness of the fit with our uniform thickness of Delrin rod and sheet.

The uniform diameter of the Delrin rod was 6.33mm, or 0.249in. We then designed 7 different holes of different diameters, intending to determine what was a tight fit (desirable for bushings), and what was a looser fit that enabled slight freedom of movement (suited for the apertures in the uprights through which the central rod was passed). We adjusted the range of the diameters to go from slightly smaller than the exact diameter of the Delrin rod to something 0.02” larger.

The parallel component of our crank handle became our test piece for the rectangular holes. Using the uniform width of the Delrin sheet as a baseline (closer to .2 than 3/16 of an inch), we again varied the holes in the test piece, changing both the vertical and horizontal lengths.

At the bottom of our test piece were rectangular cutouts that left rectangular prongs like the tines of a fork behind. We experimented by varying the distance of the gaps in between the protrusions. This was to find the best fit for the lateral supports – the equivalent of those gaps needed to tightly clamp onto the upright frame components.

We found that the circular hole with a diameter of 0.238in provided a very tight fit, and decided to use it for the bushings. The 0.241 diameter hole was a looser fit that allowed the rod to easily turn, so we chose to use it as the hole dimension in the uprights.

With our test piece of sheet width 3/16”, we found two tight fits among the eight rectangular holes we tried. Horizontally, 0.19” provided a tight fit, as did 0.37” in the vertical direction (from the top view). We then decided to combine the two to get a dimension for the hole in the crank piece attached to the rod.

Also using the sheet width, we found that 0.1875” was the best fit to snugly encompass the test piece. We then used it as the notch width for our lateral supports.  

Using our measurements, we then created the components of our windlass.

Uprights

    

We printed two of these components. The hole is 0.241" in diameter. The rectangular formations at the base are for extra height. 

Disks

 

 
This extruded version of the disk shows the four outer holes in relation to the center hole. All are uniform in radius, at 0.119" for a tight and secure fit. We printed two of this element. 

Crank parts

 

 The crank part that directly attaches to the central rod features a hole of 0.119" in radius and a rectangular hole to fit the parallel crank handle. 

 The test piece and parallel crank component.

Lateral supports

  

We created four of these lateral supports to give further stability to the frame. The notches are designed to be 0.1875" wide.

Bushings

 

These bushings were designed to fit tightly upon the Delrin rod. The radius is 0.119" and we created five bushings.

We placed the bushings along the central rod on either side of both uprights, and one on the interior of the crank part to prevent the rod and the crank from slipping around. 

Our finished 1st iteration:

Side view

Front view

Well Windlass, Post #1

When we began to design our windlass, we primarily gave thought to the task of lifting a 1L bottle of water 10cm above the tabletop. During this process, we attempted to use reasonable geometric structures to ensure weight distribution and stability. As we further refined our model, we added structural supports and other components to eliminate shakiness, finally adding parts to the base of our model to eliminate sliding. 

The Idea

In our original sketches, 1 outlines the basic structure and movement we first thought of to achieve our task. By turning the crank, the string attached to the bottle would wind around the disk component (positioned between the upright supports) and thus lift the bottle.

#2 shows our first idea for the winding mechanism. We planned to create two of such disks, and connect them through the four outermost ports with Delrin sheet or Delrin rod. The Delrin rod which was connected to the crank and passing through the uprights would be positioned through the center aperture.

#3 demonstrates our original idea for the crank component. We began by creating a handle which would fasten to the central Delrin rod. On the rectangular side of the handle, we created a hole for another piece of Delrin to pass through. This was to make winding the string easier, because of the parallel extension of the handle.

#4 shows a side view of the turning mechanism. At this point, we had determined that the four connecting supports between the disk were to be pieces of Delrin rod. It demonstrates how the string would wind about the four Delrin rods as the central rod turned.

#5 shows our idea for keeping the central rod in place: Delrin bushings. The bushings would prevent the central rod from slipping about and causing instability during the winding process.

#6 demonstrates our first idea for our upright frame components. We understood that a more triangular shape would distribute pressure and stress more than a rectangular shape. We first thought of creating triangles with the Delrin sheet.

Physics

The physics behind our design first manifested itself in the design of the upright supports. Triangles are the strongest geometric shape because a change in their angles results in a change of one or more of their sides. We chose triangular supports because of their stability.

Similar to the bottle opener assignment, the windlass required consideration of the degree of deflection in all materials. The deflection equation:

 

Where F is force, L is length, E is Young’s Modulus (stress/strain, material stiffness), and I is the area moment of inertia.

We used this equation when designing the winding mechanism. We aimed to maximize the area over which the force (weight of the bottle) was distributed. This would prevent the single beam that passed through the center of the structure and attached to the crank from breaking at any one specific point due to a concentration in weight.

Once we had brainstormed about the general “two-disks-connected-by-additional-rods” idea, we began to focus upon distributing the weight of the bottle. The central rod, being held in place through the center of the winding mechanism with bushings, would deflect to a comparable degree as the winding mechanism itself. Therefore, we aimed to minimize deflection in the winding mechanism. The force applied by the bottle was constant, as its weight remained the same throughout its ascension. The length of the mechanism was variable. We decided to shorten the Delrin supporting rods as much as we could while still maintaining a feasible width for the string to wind around. By minimizing length, we could minimize the numerator of the deflection equation.

We were unable to control Young’s modulus for the Delrin rods, as the property of material stiffness is specific to the material used. We were given a single piece of Delrin rod with a fixed diameter. The uniformity of the rod caused the area moment of inertia, or, the stiffness of the cross sectional area of it to be unchangeable. Therefore, we were able to control the deflection of the winding mechanism only by adjusting the length of the supporting Delrin rods.

Similarly, we minimized deflection in the central rod by positioning the two upright supports as closely together as our frame allowed – slightly greater than the 12cm gap between the tables.

Our further modifications to the winding mechanism kept in mind the distance of each supporting rod from the center. By increasing that distance, we would create a winding mechanism with a greater diameter, which would distribute the string across a greater area and reduce pressure on individual supports and then the entire mechanism. This also reduced the strain on the central rod.

Additions

For the winding mechanism, we decided that to have the four supporting Delrin rods close to the circumference of the disks would put significantly more strain upon the less wide areas between the rods and the outer edge. Therefore, we moved the apertures in the disks to be centered at around 70% of the radius of the entire piece. This gave us a stronger and more stable winding mechanism.

We then decided to increase the parallel component of the crank handle to a length of 4cm, thinking that an increase in torque would make turning it an easier process.

We then returned to the upright components, and decided against a completely triangular structure. We adapted the structure to look more like a “V,” and added rectangles at the base for further height.

Eliminating the base side of the triangle gave us inspiration to create lateral supports to compensate. We decided to put two on either side at equally spaced lengths apart to create three stabilizing rectangles. 

The components of our foam core model:

This part of our foam core model shows the basic upright frame structure and how the central turning rod interacts with it. The winding mechanism is also shown.

A close up of the turning mechanism. The parallel handle component was later extended to 4 cm instead of the original 2cm length.

Someone borrowed our Delrin scrap parts at the time, but we tested out our lateral support idea with the uprights nonetheless. This shows one lateral support on the lower nearer side of the frame. We then intended to place one above on the same side and to mirror the structure on the other side.