What generates force and feedback?

Description of molecular muscle mechanism - actin and myosin coupling to shorten muscle fibers.

A muscle model with parallel and series springs are made to explain the active and passive forces generated by the muscle fiber. The force curve peaks around rest-length and decreases as a muscles stretches or contracts. Explains why isometric force is the greatest, i.e. force output when muscle length is not changing.

Covered how to convert forces applied by the muscle on joints to torques around those joints. Assuming constant force, this is done by relating joint angles, bone and muscle lengths. Equating angular work with linear work \[ \tau\Delta\theta = f\Delta\lambda \], we can derive the Jacobian \( \mathbf{J}=\mathbf{\frac{d\lambda}{d\theta}} \), where \( \mathbf{\theta} \) can be a vector. Using this, \( \mathbf{\tau}=-\mathbf{J^T}f \).

Muscle afferents including golgi tendon organs and muscle-spindle afferents which act as mechanical force sensors for the muscle. The muscle-spindles are innervated with \( \gamma \)-neurons at the poles. The primary muscle spindle afferents in the central nuclear bag correspond somewhat to muscle force velocity. Secondary muscle spindle afferents in the poles correspond to muscle length. \( \gamma \)-neurons innervate the poles to change length (co-activated with \( \alpha \)-neurons for the extrafusal muscles) as a type of target muscle activation. Perfect muscles length would result in 0 change in the primary afferent firing rates.

The \( \alpha \)-\( \gamma \) afferents monosynaptic connection is important in motor feedback.

This section is important for proprioception, motor movements, and motor feedback.

Mechanisms of limb stability:

• Antagonist muscle architecture produces an equilibrium point. Polit and Bizzi experiments with de-afferented monkeys showed passive properties can reach target, but cannot resist pertubation very well.
• Passive, spring-like properties of limb promotes stability.
• CNS reflexes.
• Neuropathy - cannot sense location of limbs without vision.
• [Mussa-Ivaldi] shows stiffness of the arm remains roughly constant when expressed in terms of joint coordinates.

This site is meant to be a collection of my readings - book chapters, web articles, academic papers, etc. As such, convenient tagging is crucial. While Jekyll offers a minimalistic and fast static-site generation and convenient hosting on github-pages, it has minimal tagging support.

Requirements:

• Minimal effort initiating a new tag.
• Automatic generation of a single tag page that lists posts associated with all available tags.
• Automatic generation of separate pages associated with different tags.

There have been a few posts online about how to do this: Charlie Park, Christian Specht. The latter comes very close to what I needed, upon which I based my implementation.

Implementation:

The general approach is, whenever a new tag is created (e.g. entered into the "tags" field of a post's YAML front-matter), we need to create a tags/my_new_tag.html file with the following content:

---
layout: tagpage
tag: my_new_tag
---

This means we need to create the layout _layouts/tagpage.html.

At this point, Jekyll will have generated a separate page for our newly created tag at /tags/my_new_tag.html.

To generate the single page that lists posts associated with all tags, we create alltags.html. Note the tags will be displayed in alphabetical order.

I also want to show, for each individual post, its asssociated tags. This is done by including _includes/tag_line.html in _layouts/post.html.

Let's see how this works