In my first Ph.D. project, I robotically replicated the motion of the humerus as recorded via motion capture while subjects performed activities typical of an active amputee. The first task of this project was to program the position and orientation of the humerus onto the robot. In this post, I describe my method for accomplishing this task. To me, this is an interesting topic because it uses the same concepts as my previous post on establishing the position and orientation of a rigid body; but, the pen and paper are replaced by a robot and motion-tracking system.

The Singular Value Decomposition (SVD) is an incredibly useful tool with a staggering number of applications in seemingly unrelated fields. In this post I want to write about how the SVD is utilized to determine the orientation of a body segment from the skin markers attached to it. It's an interesting application of the SVD because it has straightforward geometrical interpretation.

Before building more complex logic into my codebase, I wanted to compare the performance of different methods of computing common biomechanics linear algebra operations in Numpy. As is common in biomechanics and robotics, I use a 4x4 homogeneous matrix to represent a coordinate system or pose, and correspondingly 3D vectors are upgraded to homogeneous coordinates. I knew that numpy.einsum could accommodate all linear algebra operations I am interested in performing, but I was curious to compare its performance against numpy.matmul for operations that could be performed just by matrix multiplication. Thanks to Numpy's broadcasting algorithm a considerable number of operation can be performed using numpy.matmul.

In Container Emulation in Python I showed how easy it is to emulate container behavior in Python in order to enable concise data access. In this post I want to talk about how this can be accomplished lazily.

The Python data model makes it easy to implement classes that allow concise data access. For example, when analyzing skin marker motion capture data, I frequently access data for a particular marker (identified by its name). Below I demonstrate how to access marker data from a trial (say arm raising and lowering) using an instance method, and via container emulation.

In this post I want to explore a simple insight about rotating between two orientations. Rotations are notoriously confusing and unintuitive, as evidenced by the fact that Wikipedia lists six different formalisms for representing rotations. Rotations are important to understand, however, because they play an integral role in physics, robotics, biomechanics, 3D animations, and a multitude of other disciplines.

When I first began studying continuum mechanics, tensors were a conundrum to me. I understood how to manipulate them algebraically but obtaining an intuitive understanding of them was a more difficult path. The purpose of this post is to simplify tensors for students who may have also run into the same roadblocks as I did. This post assumes familiarity with orthonormal bases, coordinate systems (frames), and measuring the position and orientation of one frame with respect to another.

In scientific/engineering endeavors, measuring the position and orientation of an object is important because it allows us to quantify movement characteristics. This post aims to provide a simple explanation of the process of measuring the position and orientation of an object in space. The goal is to not use any mathematical notation, although I presume that we all share a common intuitive understanding of the concept of a point and axis in the 3D space we inhabit. My failure to provide even a decent description of how to measure an object's position and orientation highlights the need for the precision introduced via mathematics (or my inability to explain a simple concepts succinctly - I pick the former). For simplicity, I will only consider measuring the position and orientation of rigid bodies, i.e. objects that do not deform.