Movement impairments resulting from neurologic injuries, such as stroke, can be treated with robotic exoskeletons that assist with movement retraining. Exoskeleton designs benefit from low impedance and accurate torque control. We designed a 2 degree-of-freedom tethered exoskeleton that can provide independent torque control on elbow flexion/extension and forearm supination/pronation. Two identical series elastic actuators (SEAs) are used to actuate the exoskeleton. The two SEAs are coupled through a novel cable-driven differential. The exoskeleton is compact and lightweight, with a mass of 0.9 kg. Applied RMS torque errors were less than 0.19 Nm. Benchtop tests demonstrated a torque rise time of approximately 0.1 s, a torque control bandwidth of 3.7 Hz and an impedance of less than 0.03 Nm/deg at 1 Hz. The controller can simulate a stable maximum wall stiffness of 0.45 Nm/deg. The overall performance is adequate for robotic therapy applications and the novelty of the design is discussed.

The average-case analysis of algorithms for binary search trees yields very different results from those obtained under the uniform distribution. The analysis itself is more complex and replaces algebraic equations by integral equations. In this work this analysis is carried out for the computation of the average size of the intersection of two binary trees. The development of this analysis involves Bessel functions that appear in the solutions of partial differential equations, and the result has an average size of $O(n^{2\sqrt 2 - 2} /\sqrt {\log n} )$, contrasting with the size $O(1)$ obtained when considering a uniform distribution.