The Problem

Lung biopsies are hard because doctors can't see the tumor during the procedure. They have to first scan the patient with CT to find the tumor, mark the spot with stickers, take the patient out, and then try to guide the needle based on that initial image. If the patient moves even slightly, they have to start over. These procedures waste hours and fail 20% of the time. Normal surgical robots can't help because their metal parts create huge artifacts in CT images, making them useless for guidance.

For my capstone project, I joined a lab building CRANE (CT-guided Robot for Needle Emplacements), a prototype that solves this using a clever cable-driven design with no metal parts inside the scanner. While earlier versions proved this could work, they couldn't move up and down and were too complex to modify easily. We focused on fixing these problems by creating a new counterbalanced design that researchers could use to develop control systems and move the project toward clinical use.

Designing a Six-Bar

To do a biopsy, doctors need to keep the needle tip in one spot while changing its angle to avoid bones and organs. The obvious solution would be an XY stage (like a 3D printer) with motors controlling each axis. But this needs multiple motors, complex software to coordinate movement, and constant position feedback. More complexity means more ways to fail and more testing needed for medical approval.

Instead, we used a Remote Center of Motion (RCM) mechanism - something that can match the CT scanner's circular shape by rotating around a fixed point. We picked a six-bar linkage because with the right dimensions, it naturally creates this motion through pure mechanics. We measured the actual CT scanner at the hospital to get the exact size we needed.

Finding the Motor Requirements

We needed to calculate how much torque it would take to move our device so we could pick the right motor. Working backwards from the needle through each joint, we found:

T_motor = (L1*W1/2 + L1*W3 + L1*W5/2 + L1*W_robot + L2*W2/2 + L2*W4 + L2*W5/2) * cos(theta)

Using 1/8" thick 6061 aluminum for our links, this worked out to about 35*cos(θ) Nm of torque, with a 35 Nm maximum. This makes sense since we're essentially asking a motor to lift a 20 lb load at around 3 ft away.

For a medical device meant to reduce procedure costs, this was a problem. Motors providing that amount of torque with medical-grade precision cost thousands of dollars. We needed to find a way to drop that torque requirement while keeping our positioning accuracy.

Counterbalancing

The obvious answer seemed to be counterbalancing. We've all seen this work - your car's trunk weighs 30-40 pounds but lifts with just a finger thanks to gas springs. However, car trunks only need to be "roughly" balanced. If the spring is a bit too strong when open or closed, it doesn't matter. You just need enough help to make it manageable. But our professor pushed harder: could we make a system that provided exactly the right amount of assistance at every position, completely negating the load on the motor?

We quickly found this was an unsolved problem. The usual solutions all had problems:

1. Torsion springs scale with kθ, not cos(theta). Additionally, even the strongest torsion springs on McMaster only hit 4 Nm - over 8x too weak for us.

2. Custom cams would work perfectly in theory, but any change in robot weight meant redesigning and remaking the whole cam.

3. Gas springs had the same fundamental issue as torsion springs - they couldn't match our cos(θ) pattern. Either too much force in some spots or too little in others.

After burning through the standard approaches, we found something called a gravity arm. By running a cable from an extension spring to the arm, the spring moves exactly with the robot, giving us the cos(θ) relationship we needed:

T = hkr*cos(θ) where:

• h = pulley height

• k = spring constant

• r = distance from pivot to cable

• θ = angle from horizontal

Perfect balance happens when hkr equals our load torque (35 Nm). But normal gravity arms put the pulley right above the pivot point. This means the arm can only swing one way - try to go the other way and it hits the pulley tower.

A Novel Bidirectional Approach

We realized we could make the system work both directions by mounting the pulley in the center of the linkage and below a crossbar. A quick prototype using laser-cut wood proved this worked - the linkage stayed balanced at any angle, moving smoothly with just a light touch.

But adding this gap between the pulley and crossbar turned our simple cosine equation into something much nastier:

T = √2 k_eff √(r²cos(2θ) + r² - 2rx_gapsin(2θ) - 2ry_gapcos(2θ) - 2ry_gap) × √(-x_gap²cos(2θ) + x_gap² + 2x_gapy_gapsin(2θ) + y_gap²cos(2θ) + y_gap² + 2z_gap²) × |(a_gap - r)(√(x_gap² + y_gap² + z_gap²) - √(-2r²sin(θ) + 2r² - 2rx_gapcos(θ) + 2ry_gapsin(θ) - 2ry_gap + x_gap² + y_gap² + z_gap²))| × 1/(2√(-2r²sin(θ) + 2r² - 2rx_gapcos(θ) + 2ry_gapsin(θ) - 2ry_gap + x_gap² + y_gap² + z_gap²))

While our prototype stayed balanced thanks to its high friction-to-weight ratio, calculations showed this would lead to 7.5 Nm of error with our real 20 lb robot. Better than our original 35 Nm problem, but not ideal.

Numerical Optimization

Most counterbalance designs just try to get zero torque at the extremes where the Torque is highest (0° and 180°). However, this leads to large errors in the middle - exactly where we needed precision for medical procedures. So we wrote code to minimize average error across the entire range of motion.

Our optimization revealed some weird but useful combinations of spring constant (k), pulley height (h), and cable attachment point (r). Playing with these parameters got our maximum torque error down from 7.5 Nm to 4 Nm.

Spring Selection and Safety

The real challenge came when selecting actual springs. Our first design used an 11.2 lbf/in spring, producing about 100 lbf of force. This presented an unacceptable safety risk as we would essentially be working with garage door springs which require routine inspection and are dangerous to say the least…

The required spring parameters are roughly linked through:

k = T_robot/(h*r)

This created a three-way balancing act:

1. Minimize force in the system (F = k*√(r² + h²))

2. Keep the spring under its max load (F_max)

3. Keep the gap between pulley and crossbar small (r - h)

Instead of focusing on individual parameters, we realized what really mattered was the ratio between the maximum load and spring stiffness. After sorting through McMaster's catalog, we found a 4.4 lbf/in spring that could provide the same torque with much lower forces - around 50 lbf instead of 100 lbf.

Analysis-driven Design & Coupling

The most interesting and difficult part about this project was how interconnected everything was. When we switched from the 11.2 lbf/in to 4.4 lbf/in spring to make the system safer, it forced changes through the entire design.

The spring needed to travel further to get the same force, so we had to move the mounting points outward. This made the pulley tower grow from 6" to 9.5" tall. The taller tower meant redesigning the crossbar to maintain clearance. New geometry meant adjusting all six link mounting points to keep our motion path. The base plate had to get bigger to handle the spring travel. The bigger base needed new manufacturing methods since it wouldn't fit our CNC. Even the wire rope needed to be recut for the new pulley positions.

To keep the project on schedule while dealing with all these connected changes, we built things in a specific order:

1. Started with the most constrained parts

2. Built outward to the bigger components

3. Left adjustable parts until final integration

CAD & FEA

We first designed and analyzed our system in SolidWorks, updating when needed.

Manufacturing

When we had a final design and were ready to manufacture, we started with the bearing housings since they were the most precise parts of the system. Their actual dimensions drove adjustments to everything else - better to adapt to real numbers than hope everything matched perfectly. These needed:

• 0.0005" tolerance on bearing seats

• Perfect alignment between multiple bearings

• Surface finish good enough for press fits

The base plate was too big to fit our CNC mill in one setup, so we had to do multiple operations. The tricky part was keeping alignment between setups - critical features needed to line up perfectly. We solved this by making one edge our master reference and designing fixturing to hit that edge every time.

The whole 6-bar's performance came down to tolerance stack-up. Get one bearing a few thou off and the friction would increase. We had to watch:

• Bearing alignment between housings - any misalignment meant binding

• Link lengths - small errors compound through the mechanism

• Assembly clearances - too tight means binding, too loose means wobble

We ended up using 6061-T6 aluminum for most components due to its high stiffness-to-weight ratio, machinability, and cost. For some key structural parts, we used stainless steel for its strength.

Each of our components also had to handle the spring forces safely. We purchased key parts to ensure a high factor of safety:

• 3/16" stainless wire rope (600 lbf capacity)

• Plug lock end fittings (600 lbf capacity)

• Compression sleeves (600 lbf capacity)

• All stainless to avoid corrosion issues

Motors & Drivers

Our motor system needed to meet two three requirements: drive the counterbalanced six-bar lift, provide closed-loop control for precise positionining and operate at a speed of 5 cm/s at the end effector. This naturally led us to servo motors with integrated encoders. Maxon Motors - the standard in robotics - offered an ideal solution with precise position control. However, with month-long lead times, they fell outside our project scope. We ended up wiring up some spare motors in the lab to provide a test bench for the concept in the meantime.

Results

We finally finished manufacturing and assembly at 6am after an all-day shop session. The final design required 28 press fits! When we finally got it together, the counterbalance worked better than our calculations predicted - friction alone held the linkage steady at any angle. The whole mechanism, despite weighing over 20 pounds, moved smoothly with just a finger's worth of force. This was the kind of controlled motion we hoped to achieve, and it was awesome to see all of the theory work at this scale in person.

Presentation

We presented the project at both UCSD's Capstone Demo Day and at the Advanced Robotics & Controls Lab, where it generated interest due to the scale of our project and the novel approach we took.

Here is a team picture:

A picture of our poster:

And us at graduation!