Robotic gait retraining systems typically function by employing mechanisms that move a patient’s lower limbs in a controlled manner. In this paper, an end-effector gait retraining system was designed, utilizing a 2-PRR mechanism (PRR refers to the structure of each robot’s limb, consisting of an active prismatic pair (P) and two passive rotational pairs (RR) pairs). The mechanism, which corresponds to a parallel robot, was synthesized through visual design tools (design atlases) to evaluate performance indices, such as the workspace size, local and global conditioning, and mechanism stiffness. Quasi-static force analyses were conducted to calculate worst-case scenario operational loads. These loads were then used to obtain a valid cross-section geometry that would withstand static stress, buckling failure, and fatigue failure.

Collisions are a key topic in physics and engineering education. An experiment with multiple body one-dimensional collisions is presented, aiming to measure relevant physical quantities by tracking the motion of the system of particles during the collision. Relations between different physical quantities can be explored in the experiment, such as linear momentum, impulse, and energy. Equations are presented for modeling velocity changes during the collisions under the elastic and inelastic conditions and extensions to many body colliders can be easily implemented. Predictions for the velocities and other collision quantities were verified for a set of mass parameters by photogrammetry and digital video analysis.

Derivative enhanced Gaussian Processes (DEGPs) can significantly improve surrogate model accuracy over standard Gaussian process (GP) formulations by incorporating derivative information. However, standard implementations scale poorly with dimension, limiting their use in high dimensional engineering problems. JetGP is a Python framework that unifies existing derivative enhanced GP methodologies into a single library and extends them to support arbitrary order derivative information. The library implements four complementary formulations: standard derivative enhanced Gaussian processes (DEGP), directional DEGP (DDEGP), generalized directional DEGP (GDDEGP), and weighted DEGP (WDEGP). By unifying these approaches in a consistent interface with robust numerical implementations, JetGP enables practitioners to balance predictive accuracy and computational efficiency for high dimensional optimization, uncertainty quantification, and sensitivity analysis in engineering design.