Lecture notes on specific topics.

## Quaternions in Kinematics: BYU Lecture

Students at BYU formed a study group advised by Prof. Denise Halverson to explore Kinematic Synthesis. They invited me to join them to discuss Quaterions and how they are used in Kinematics.

I have not talked about this material in some time, so it was interesting pulling together the theory from many past talks, but I soon became afraid that I was assembling a short course, not a lecture. So I took a different approach.

Here is a video of the lecture. The notes that I prepared are posted below.

My Quaternions in Kinematics presentation is posted here.

## Introduction to Linkage Synthesis

This introduction to the graduate course ME 322 Kinematic Synthesis of Mechanisms shows the potential for design innovation using a mathematical formulation to compute the dimensions of a device from its required task, literally the calculation of its form from the desired function.

## Curvature Theory for Planar Point Trajectories

These notes for the Stanford University graduate course ME 322 Kinematic Synthesis of Mechanisms present the curvature properties of point trajectories in a planar moving body such as the coupler link of a four-bar linkage.

Update:  December 13, 2017. These notes have been revised to use the notation for the components of the pole acceleration and rate of change of acceleration to match Bottema and Roth’s Theoretical Kinematics.

## Four-bar Linkage Synthesis, Two and Three Task Positions

These notes for the Stanford University course ME 322 Kinematic Synthesis of Mechanisms introduce the synthesis of a four-bar linkages that guide the coupler link through two and three specified task positions.

December 12, 2017.  These notes have been revised to introduce Sandor and Erdman’s formulas for linkage synthesis which solve for the input and output cranks.  This provides a nice pairing with the related equations that are solved for the fixed and moving pivots, directly.

## Four-bar Linkage Analysis Notes

These notes have been prepared for the Stanford University graduate course ME 322 Kinematic Synthesis of Mechanisms.  This first set details the position and velocity analysis of a four-bar linkage.

Update:  December 12, 2017.  These notes have been revised to represent rotation matrices using boldfaced letters.  Remarkably, because 2×2 matrices commute this allows these matrices to be replaced by complex exponentials and the coordinate vectors to be replaced by complex numbers and the derivations and calculations do not change.

## Type Synthesis, Assur Groups, and Rigidity

These lecture notes introduce students to research on classifying linkage systems which involves a variety of ideas such as Assur groups, Baranov trusses, and Rigidity theory.  Organizing the increasing complexity of machine systems to guide inventors has attracted researchers for literally generations and has generally been called “Type synthesis.”  The goal is to provide a systematic way to explore the types of linkage systems that are available to address a design need.

## MK.1 Mechanical Computer

Nicholas Bodley sent me to www.maritime.org for information about the MK.1 mechanical computer that he used as a Navy Fire Control Technician during the Korean War. Just the schematic of its operation is a dizzying flowchart.

A description of the mechanical components of this computer system can be found in the manual Basic Fire Control Mechanisms (62.7MB). It is an excellent description of the use gears, cams and linkages for computation.

MK 1 Mechanical Computer

## Four-bar function generator: Open a door

Four-bar function generator

Select this link, Four-bar linkages, for a Geogebra book that illustrates linkages ranging from a lever to a crank-rocker that open a door. This includes the construction of a four-bar linkage that coordinates the open and closed positions with specific input crank angles, called a four-bar function generator. The iPad application, MechGen FG, computes four-bar function generators for five coordinated values of the input and output cranks.

## Kinematics Summer School

Profs. Carl Nelson and Anurag Purwar organized a Summer School on Kinematic Theory at the University at Buffalo, New York as part of the 2014 ASME Design Engineering Technical Conferences. Please select this link to get access to all of the talks: Kinematics Summer School.

My lecture on the synthesis of six-bar and eight-bar linkages is the third item on the playlist.

You can access a pdf of my talk at the link: Synthesis of Planar Six-bar and Eight-bar Linkages.

Among these is a nice presentation by Anurag Purwar on Quaternions and Clifford Algebras.