I. Introduction And Background

The Final Project for Robot Mechanism Design was to apply the concepts learned in the class to a new mechanism and to physically construct this mechanism.

To achieve this, our team chose to explore complicated ways in which a simple box can open. We brainstormed various paths that the lids of a box could follow, and filtered for ideas with the following characteristics:

• Unexpected.

• Non-obvious mechanism.

• Can be accomplished with a closed linkage.

The brainstorming resulted in a plethora of options:

The movement that we settled on was described in our proposal with the following illustration:

It was felt that this was novel and did not have an obvious implementation. Based on early feedback from the Professor, we wanted to achieve this motion with a single motor.

It is important to note that the decision for this shape of movement was made before any effort was made to research what mechanisms might achieve the movement, or even whether the movement was possible. We felt that this represented the purest purpose of the assignment: inventing a mechanism, from scratch, to meet a desired objective.

II. Design Process

Steps Along The Way

Our work consisted of an unending stream of designs, prototypes, failures and changes. Here we document the overall story arc of how we arrived at our final design, offering this as a view of what was learned.

The hardest part of the design was finding mechanisms that could make this motion. The earliest ideas were 6-bar mechanisms with folding/expanding arms on both the front and back edges of the lid. We weren't sure how we would control the arms in this motion. Presumably a further 4-bar loop would have been necessary to power these arms through their synchronized dance. 

Front Edge On A Slider

It wasn't long before we changed to having a slider to guide the front edge of the lid, as shown in this early sketch and Solidworks model:

The advantage of a slider is that the lid's motion could be kept "square", with a right-angled corner. We didn't want the front edge of the lid to dip down into the volume of the box, as this would make the box impractical for holding anything. This was the closest to the proposal movement, and guided our design trade-off decisions throughout. 

At this stage in the design, most of the mechanisms we imagined powered the back edge with the motor, and allowed the front edge to be dragged along the slider. This left us with a large problem: how to cause the front edge to turn the corner and go down the other arm of the slider? Once the slider had been pulled to the corner, and the powered back edge reversed directions to push the slider, what would make the slider choose one path over the other?

We explored ideas of mechanical toggles that would alternate the preferred direction every time the slider passed through. We considered using a second actuator (usually imagined as a solenoid pusher) to steer the slider in the right direction. None of these ideas seemed satisfactory.

Power The Front With Expanding Crank; Back Becomes A Slider

This challenge was instead solved with a change to powering the front edge of the lid around the full 90 degree motion, and making the back edge of the lid a passive follower. Being passive, the back edge would require more structure, and so it was changed to a slider.

To power the front edge, we added a crank around a low, central pivot. Which introduced a new problem: how to keep the slider path with a square corner if it was to be driven by a revolute joint with a crank? We considered ways to use a two-link crank+coupler to push the slider, but didn't find a way to make this work in our constraints. In the end, two links were used, but in a slider configuration that allowed the length of the combined crank to change, but the angle between the two component links would be kept fixed.

The first physical prototype we built used a back edge slider in a vertical channel, a front edge slider in a right angle (with a slightly rounded corner), and a crank with an expanding slider. This prototype worked, but required manual intervention to keep all parts of it moving. It had a tendency to bind with friction.

Slot Angles

The next big innovation in design was to change the back edge slider angle so that there was less resistance to the motion. In the previous design, with a vertical path, the force is initially pushing the back slider directly into the wall at 90 degrees – expecting it to move was misguided. Even once the slider was out of this initial 90 degree angle, the normal force of the slot generated excessive friction. By tilting the slot, the normal force on the side of the slot was reduced, and at least some of the driving force was in the desired direction of movement.

We continued tilting the back edge slider until the distance between the back edge of the box (the leftmost of the back edge slider) and the path of the lid (the right-angled slot) was too large to be reasonable. This would represent wasted empty space, outside the enclosure of the box, but within the bounding volume of the walls.

Crossing Sliders

Which led to the next innovation: slot paths that crossed on different z-planes. We moved the back-edge slider to the far side of the wall, and used a metal rod as the slider path instead of a slot in the wall. Now we could angle the back edge path as much as we wanted. This allowed continued reduction in the normal forces in the slider, reducing friction.

 

 

Curved Slot

We were also able to improve the angle of the front-edge slider. Instead of a right angle, we introduced slope throughout, so that it was never quite vertical and never quite horizontal. We also increased the radius of the corner curve, where the prototypes tended to get stuck (because of the friction of the normal force). In practice we settled on a spline curve that kept as much of the right-angled motion as possible, while allowing the mechanism to function. Because this spline was quite complicated mathematically (we used more than 50 points on the spline), we performed our mathematical analysis with an approximation of an arc centered away from the crank pivot. This allowed a reasonable match to the spline, still allowed for the crank length to change, and included enough mathematical challenge to be interesting.

Making It A Box

This is when we first started to turn the "quarter box" we had been making for prototypes into a full box. We knew that the physical box, with interlocking fingers, was a common design, and were not concerned with it. What changed in our minds at this point was adding the third dimension – our "lid" had been represented by a flat link in all our designs up until this point.

The motor was to be directly connected to the crank pivot on one side, and the other side of the lid was to be an identical copy of the sliders but without a crank to power it. We expected these sliders to be pulled along their path by the lid itself.

The first 3D prototype disabused us of this belief. With the torsion across such a long link, with the play we would necessarily have in our joints and bearings, the passive sliders would lag behind, and would bind against the bearing/slot.

Dual Powered

We quickly changed to powering both ends of the lid. The motor was moved to a central location, and a drive shaft and gear train used to move the power to the cranks at both ends. (This made both ends of the box identical mirrors.)

Once the power was being delivered symmetrically, the sliders moved much more synchronously, which reduced torsion and binding. Despite this, the flexibility of the lid meant that the sliders were still twisting too much and continued to bind.

Rigid Cross Beams

The final major change was to add rigid steel cross beams from one side of the box to the other. These beams took on the functional role that had previously been performed by the lid, and did so with much more rigidity. It enabled us to keep the sliders in place without having retaining caps, as they were being pushed into both walls from the center, so the curved slider became a simple pin. The cross beams were also easier to integrate into the 3D printed joints, with more "one-piece" elements. 

Final Design

The final design consists of:

1. A curved slider for the front edge of the lid, implemented as a pin-in-slot.

2. A straight slider for the back edge of the lid, implemented as a moving rod sliding through bearings.

3. An expanding crank slider to power the front of the lid, implemented as a steel rod lower crank sliding through a linear sleeve on the upper crank.

This is all powered by:

1. A gear integrated with the crank pivot.

2. A gear attached to the drive shaft, and interacting with the crank gear.

3. A drive shaft running across the box to a mirrored mechanism on the other side.

4. A drive gear on the drive shaft.

5. A pinion gear on a motor, pushing the drive gear and thus the drive shaft.

And all controlled by:

1. An Arduino Uno applying simple control algorithms.

2. User buttons for "open" and "close" motions.

3. A power switch to turn power to the Arduino on and off.

4. A 9V battery power source.

And the whole thing is wrapped in an outer layer that makes up the box.

III. Kinematic Analysis and Synthesis

Note: this section is unchanged from our earlier analysis submission.

Schematic Description

The mechanism can be viewed schematically like this:

The crank is on a revolute joint with ground at point "O2". The crank contains a slider which allows the length of the crank to vary passively. For analysis, we consider this to be a fixed-length "Link 3" of length "b", and a variable-length "Link 2" of length "a", and they meet at point "A".
The crank connects to a pin in a slider at "B". The slider follows a curved trajectory instead of the usual straight line. We consider "Link 4" of length "c" to be the straight-line distance between point "B" on the slider and an imaginary ground point "O4", roughly at the bottom end of the slider's slot.
The lid of the jewelry box is also attached to the slider at "B" with a revolute joint. It makes up "Link 5" of length "f", after which it attaches to point "F" through a revolute joint.
Point "F" is on another slider, this time following a straight-line path. We imagine "Link 6" of length "g" to reach to "O6" at the bottom end of this slider path.
We imagine ground "Link 1" of length "d" between O4 and O2, and "Link 7" of length "h" between O4 and O6.