Question 2 of 7: Additive manufacturing and a transtibial prosthesis

Question 2: Additive manufacturing and a transtibial prosthesis (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The product selected is item iii, the prosthetic leg, and specifically its transtibial (below-knee) socket — the one component that is unavoidably unique to a single patient. The comparison is between the conventional route (plaster cast, hand rectification, vacuum-laminated composite) and a laser-sintered PA-12 socket printed from a 3D scan. Costs are per socket in Canadian dollars.

Find. The functional, process and manufacturing consequences of the additive route, including the annual volume at which the two routes cost the same.

Approach. Treat functionality, design process and manufacturing separately, and settle the manufacturing half with the standard tooling-amortisation model c(n) = T/n + u, which is the one piece of arithmetic that decides where additive manufacturing belongs.

Part A — Impact on functionality (6 marks)

The socket is the interface across which a patient’s entire body weight passes into the prosthesis, through a residual limb that has no anatomical business carrying load. Fit is therefore not a comfort issue but the determinant of whether the device is worn at all, and the functional gains from additive manufacturing all follow from the fact that geometric complexity is free.

First, true patient-specific geometry. The socket is built directly from a 3D scan of the residual limb, so the internal surface can follow the actual anatomy rather than a rectified plaster approximation of it. Second, and more important, spatially graded stiffness: the wall can be printed as a lattice whose cell size and strut thickness vary across the surface, stiff over load-tolerant regions such as the patellar tendon and popliteal fossa, and deliberately compliant over the bony prominences — the tibial crest, the fibular head, the distal tibia — where pressure causes the ulceration that takes a prosthesis out of service. No subtractive or moulding route can grade a property continuously through a wall in this way; the conventional laminate is uniform and relief has to be carved into the shape instead.

Third, integrated features at no assembly cost: ventilation channels through the wall to manage perspiration, the pyramid-adapter interface printed as part of the socket rather than bonded on, and a lattice that carries the strain-gauge or sensor routing internally. Fourth, mass: 0.780 kg conventionally against 0.520 kg printed, a saving of 0.260 kg, or 33 %. Distal mass on a prosthesis is disproportionately expensive metabolically because it is accelerated and decelerated twice per stride, so a third off the socket is felt directly as reduced fatigue over a day’s walking. Fifth, a functionality that is not physical at all: the socket geometry now exists as a file, so it can be reprinted at any time as the residual limb changes shape, which it does substantially in the first year after amputation and again with weight change.

Part B — Impact on the design process (5 marks)

The design process for a socket is an iteration loop, and additive manufacturing changes the cost and duration of the loop rather than the loop itself. Conventionally the prosthetist casts the limb, rectifies the positive by hand, laminates a transparent check socket, fits it, marks it, and repeats: three iterations at roughly five working days each, so about 15 days elapse before a definitive socket is released. Printed check sockets can be produced overnight from a modified file, and the same-day fit-and-adjust cycle brings that to roughly one day. The 14 days recovered are not merely convenient; they are the difference between iterating while the patient is present and iterating across separate appointments, which is what limits the number of iterations in practice.

Three further effects matter. Design freedom moves upstream: because tooling no longer constrains the geometry, the designer can carry two or three genuinely different socket architectures into physical trial instead of committing to one on paper. Design becomes parametric: rectification is a set of numerical offsets on a scan rather than plaster removed with a rasp, so a change is recorded, reversible, and transferable to the next socket for the same patient. And validation moves earlier: a printed socket can be instrumented and gait-tested during concept development, so the design is validated against measured interface pressure rather than against the patient’s verbal report. In Ulrich and Eppinger’s terms the technology compresses the concept-development and system-level design phases into one another, and shifts effort from detail design to specification.

Part C — Two major impacts on the manufacturing process (4 marks)

Impact 1: the cost structure loses its tooling term, which inverts the economics of low volume. Conventional production carries capital and tooling T that must be spread over the annual volume n, so its unit cost falls with volume, while the additive route has no tooling and a flat unit cost:

Setting them equal gives the break-even volume:

At 60 sockets a year the conventional route costs 430 against 380, and additive wins; at 240 it costs 355 against 380, and conventional wins. A clinic fitting a few dozen patients a year is unambiguously on the additive side of the line, and a national manufacturer is not — which is the general result. Additive manufacturing does not make things cheap; it makes unit cost independent of volume and of complexity, and that is only an advantage below the break-even point.

Impact 2: quality assurance shifts from inspecting the part to qualifying the process. A laminated socket is made by a technician whose skill is the control; a printed socket is made by a machine whose build parameters are the control, and its properties are anisotropic — strength across the build layers is markedly lower than in-plane, so orientation on the platform is a design decision, not a production convenience. The manufacturing process therefore acquires obligations it did not have before: powder lot traceability and re-use ratio limits, witness coupons built alongside each socket and tested to prove that build’s properties, controlled post-processing (de-powdering of internal lattices, thermal treatment, surface sealing so the porous surface can be cleaned), and dimensional verification of a part with no datum faces to hold. For a Class I or II medical device in Canada this is a documented, validated process under the Medical Devices Regulations, and the effort saved in fabrication is partly spent again in qualification — an honest answer says so.