4.2. Prototype

Table of Contents

Prototype Overview 

The prototype centered around exploring mechanisms for the finger movement and confirming the motion of the arm. The baseline design for the finger mechanisms is defined as Idea #1 below, where there is a single crank that controls three slider blocks. A finger will be attached to each slider so the movement of the slider block directly causes the finger to move into the hand and out. Idea #2, defined below, is more complicated, and the prototype work aimed to validate the movement profile. This iteration consisted of an addition to the slider block of another 4-bar, back-driven slider crank, where the slider motion caused the finger to rotate from pointing down to pointing forward. 

Final CAD Images 

The image below presents the final CAD assembly for the prototype. Green shows the arm 4-bar mechanism, the orange/brown is the palm, the yellow shows the initial slider crank mechanism (sliding in the purple sections), and the light blue represents the finger slider-crank. All mechanisms are described further throughout the assignment. Note that the prototype currently incorporates a friction joint for the slider but will likely be transitioned to linear bearings for the final product. This is currently in the “scissors” position.

Iteration Documentation - Design 

Arm Mechanism 

For the arm mechanism, two primary configurations were considered. Note that the initial 4-bar presented in the mechanism is not pursued further since it does not incorporate both the forearm and the wrist movement. The two ideas that were considered in this phase are presented below: 

Idea 1: Sixbar Crank 

Ideas 2: Tertiary 4-bar 

After CADing both options and animating their movements, Idea 2 was chosen to move forward with. This idea was much simpler from an analysis standpoint, and still allowed similar variability in the tertiary mechanism to create different forearm (AB) and wrist (BC) motion profiles. It also decreased the number of moving joints and moving parts, reducing the likelihood for variability and slop. The tertiary joint will also be more stable for the heavy hand. 

Finger and Hand Mechanism 

Throughout the prototyping process, we considered two different configurations for the hand and finger mechanisms. Both are analyzed in the Kinematic Analysis section. 

Idea 1: Sliding Fingers

The initial idea is based on a direct correlation between the position of the sliders and the extension of the fingers. An initial MotionGen model is shown below. A single crank on the “palm” of the hand will be connected to three linkages that all connect to their own slider lock. The angle of the slider slots and the length of the fingers will be varied so that as the crank rotates, there is a location where each rock, paper, and scissors state occurs. Though not directly shown, fingers would connect each of the three linkages and extend out of the hand (in the plane shown). 

Idea 2: Rotating Fingers 

This idea represents a supplement to the above mechanism. This would be on a different plane than the above mechanism, and the movement of the slider block would instead cause the purple linkage to rotate around its fixed point. This serves to create a more realistic motion of the fingers”bending” and moving down to contract, and then rotating to extend. This mechanism is also beneficial because a smaller slider distance is required to get the same “extremes” as the above idea. 

Kinematic Analysis 

Arm Crank Position Analysis 

Iteration #1

Iteration #2

After printing out a first iteration of the hand and the arm (see below in Iteration Documentation - Build), it became clear that the arm needed to be sized up significantly, by a factor of 1.5. This scaling up matches the final dimensions of the hand shown in the final CAD images, defined by matching the distance from B to P on the tertiary link to the bottom dimension of the palm. Point P therefore represents what we expect the bottom of the hand to be doing. 

Finger and Hand Mechanism Position Analysis

Hand / Sliding Finger Mechanism (Idea 1) 

The first approach for the hand mechanism was based on achieving a visual representation of rock, paper, and scissors. A simple method was chosen by utilizing three slider-crank mechanisms positioned at different angles, all driven by a shared crank input. To develop a suitable model, the mechanism was simulated in Motiongen, and the link lengths were adjusted until all three states could be demonstrated within a single crank rotation. After achieving accurate link lengths, a design was modeled in CAD.

Idea 2: Additional Finger Mechanism 

The approach to actuate each finger was built upon the hand mechanism by coupling an additional slider-crank mechanism to the prescribed sliding motion. In this case, the linear motion produced by the hand mechanism was used as the input, while the rotation of the finger link was treated as the output. To achieve the output goal of turning each finger 0° to 90°, Motiongen was utilized to determine the ideal distance the slider should travel. This resulted in scaling down the original hand mechanism linkages to fit the desired slider length. After revising the CAD to include both mechanisms, a print was completed and evaluated (see Final Prototype).

As described in Iteration Documentation - Build, the motivation for prototyping this design was due to the fact that Idea 1 resulted in a very large and wide hand. Therefore, several modifications were made before printing the final prototype. Specifically, all three slider-crank mechanisms in the hand mechanism were scaled down to achieve a more realistic palm size. Additionally, the placement of the fixed point was shifted to be closer to the sliders in the finger actuation mechanism as illustrated in the diagram below.

The above position analysis illustrates the positions of each slider block on the hand for any position of the crank. Note that this uses the updated hand slider dimensions from adding the rotating finger mechanism. A general location for each distinct state is marked. For paper, the sliders all have very little displacement (contracted fingers), for rock, they are all very extended, and for scissors, two of the fingers are extended more than the other.

Velocity Analysis of Fingers 

This is the velocity analysis of the hand mechanism; the graph shows the velocity of the end of the finger based on the angle of the crank. The fingers each have varying velocities based on their position and distance from the crank. The left finger is the farthest from the crank, so its position changes faster than the others, and therefore, it has a higher velocity. 

Force Analysis of Arm

The force analysis of the arm at the moment depends on the exact motor we choose since the torque output of the motor/force input into the four bar will vary. The equations used are from the lecture slides for a four bar, just like our arm. 𝜇 is defined as theta4 - theta3 while 𝜈 is defined as theta2 - theta3. This four bar is considered to be in an open configuration, and the position analysis that feeds into the mechanical advantage follows this.

A plot of the mechanical advantage is shown below. The mechanical advantage flips from positive to negative because of the directions of the input and output force in the coordinate system. Between ~60º and ~250º degrees, both forces are negative relative to the CS, making the mechanical advantage positive overall. The discontinuity/hole is attributed to when the rotational velocity ratio w4/w2 is zero.

Animation of Arm

Below is the link to the CAD animation of the 4-bar arm mechanism, with the crank going through its full rotation. The tertiary linkage encapsulates an up/down movement of the arm as well as an offset up/down motion in the wrist. 

Arm Animation.mp4

Animation of Hand / Fingers 

Initial consideration of the hands and fingers was done in MotionGen. These videos are presented as a preliminary, 2D motion animation. 

finger_actuation_recording.mp4

hand_mechanism_motiongen_animation.mp4

Below is the link to various CAD animations including the hands and fingers. First is only the hand sliders, with pauses to generally show the rock, scissors, and paper positions. This forms the base idea for the rotating fingers idea (#2) and the overall motion profile for the sliding fingers iteration (#1). Second shown is the rotating finger slider connected to the hand slider. This shows the tip of the finger moving through its range of motion as the hand slider moves back and forth. Finally, the full motion profile for the hand and the rotating fingers is shown. Note that only a partial rotation is shown, as Solidworks seems to be having constraint issues and will jump to a new position when moving past this point. Further work will be done on the connection between the hand slider block and the rotating fingers to ensure the fingers range of motion is limited to the desired angles for either closed or open. 

Hand Slider Animation.mp4

Single Finger Animation.mp4

Full Hand Animation - Iteration #2.mp4

Mobility Calculations 

Grashof conditions and the Gruebler equation are applied to the final iterations of the arm, the hand slider, and the finger slider. Both of the sliders are still 4-bars, so the fourth linkage is the slider block itself, and the ground link goes to infinity. No Grashof is calculated for the slider mechanisms, as it does not match the typical longest/shortest link configuration. 

Gruebler: M=3(L-1)-2J1 -J2

Grashof: S+LP+Q for Class 1 

Arm: 

Gruebler → M=3(4-1)-2(4)-0=1 DOF

Grashof: S+L=2.16+9=11.16;   P+Q= 7.95+7.125=15.08

S+LP+Q → Class 1, shortest link can make a full revolution 

Hand Slider:  

Gruebler → M=3(4-1)-2(4)-0=1 DOF

Finger Slider: 

Gruebler → M=3(4-1)-2(4)-0=1 DOF

Iteration Documentation - Build 

First Laser Cut Attempt 

We completed an initial laser cut of all our components. Images are shown below. For the arm, this was scaled down to function as a proof of concept, since this is a typical crank 4-bar with a straightforward motion profile. We primarily wanted to ensure that the tertiary mechanism functioned correctly to create different up/down motions for the forearm and the wrist. 

For the hand and fingers, the initial version used the configuration where the fingers were directly tied to the slider blocks, so the displacement of the end of the finger was the same as the displacement of the slider block. This is the simplest form of the fingers, but it meant that the hand was quite large. We printed this initial configuration to get a better idea of the tolerance for the sliders and how we could scale down the palm. We realized that the size of the palm was defined by the length of the sliders, which were quite long to create a clear distinction between closed and open fingers. Therefore, as described above, we attempted another iteration where the slider block is used as the input for another 4-bar mechanism that rotates the finger from pointing straight to the bottom to pointing straight forward (90-degree change). Additional changes with slider and hole tolerance will be made. 

Overall, we had issues with the laser cut dimensions. There seemed to be slight tolerance issues where different laser cut linkages had ~ 10% differences in hole size and width. The arm coupler was also too small, likely due to a unit issue in the CAD or an importing/scaling issue to the laser cutter. Moving forward, we will double check the laser cut imports to ensure that the width for all of them is 0.5 inches, and manually scale them up if not. 

Physical Prototype Images 

Below include images of the final physical prototype presented in the demo. Note that this includes the rotating fingers iteration, all manually powered. 

Preliminary Bill of Materials 

Next Steps and Conclusion 

The prototype and demonstration proved that the arm crank functions as expected. The hand slider also has the correct movement profile, and we were able to clearly see distinct states for the rock, paper, and scissors. Motion was quite difficult for the sliders, so we will plan to shift to linear bearings instead of a friction-based joint. Spacers will also need to be printed for the final product to ensure no interference and planar motion. The rotating finger mechanism, however, did not entirely function as anticipated. The fingers do not seem to be constrained to a 0 to 90 degree rotation, and try to penetrate through the hand. Moving forward, we will complete analysis of the rotating fingers to get a global position of each fingertip to verify if this is a design or assembly problem. If we are not able to adjust link lengths to obtain the desired motion, we will move forward with our baseline sliding fingers idea.