Background:​ An Instrumented Spatial Linkage (ISL) was developed to measure changes, caused by total knee arthroplasty (TKA), in the two kinematic axes of the tibiofemoral joint:​ the flexion-extension (F-E) axis and the longitudinal rotation (LR) axes. The objectives were to 1) determine both the optimal size of an ISL and position of attachment to the joint and the best pattern of applied motion such that measurement errors are minimized, and 2) construct, calibrate, and validate this ISL.

Methods:​ A mathematical model of a virtual ISL that measured motion across a virtual tibiofemoral joint was created in MATLAB. Both the best pattern of applied motion and the best ISL size and position were determined, which minimized the position and orientation errors due to common encoder errors. The optimal ISL was constructed and calibrated using a novel method. Validation was performed using an adjustable fixture to quantify the error in measuring changes in the F-E and LR axes.

Results:​ The optimal ISL was determined and an ISL was constructed following those guidelines. The best pattern of motion was determined and used in the subsequent validation. For the calibration, the resulting root mean squared errors were each below 0.29% of the respective full-scale range. When measuring changes to the F-E or LR axes, each orientation error was below 0.5 deg. When measuring changes in the F-E axis, each position error was below 1.0 mm.

Discussion:​ The mathematical model developed herein could be used to determine the errors for any ISL size and position, any applied motion, and potentially any anatomical joint. Despite the large size of the ISL, the calibration residuals were better than those for previously published ISLs. Validation demonstrated that this ISL is capable of accurately measuring clinically important changes in the F-E and LR axes.