Lecture notes on specific topics.

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.

Update: This is the final version of the  lecture scheduled for January 9, 2018

T1 Introduction to Kinematic Synthesis-small
Curvature Theory

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.

T3 Curvature Theory revised v2
T2 Two and Three Position Synthesis

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.

Update.  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.

T2 Two and Three Position Synthesis revised v2

 

 

T1 Four-bar Linkage Analysis

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.

T1 Four-bar Linkage Analysis revised
Type synthesis

Type Synthesis

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.

Type Synthesis
MK1 Schematic

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

MK 1 Mechanical Computer

Four-bar function generator

Four-bar function generator: Open a door

Four-bar function generator

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

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.

Select this link for a YouTube playlist of the videos of each presentation.  

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.

Introduction to Linkages

Introduction to Linkages

Introduction to Linkages

Introduction to Linkages

Please select this link to open the Geogebra Book containing constructions of a number of interesting linkages. This is an introduction to the useful movement available with articulated systems.

Mechanical Advantage

Mechanical Advantage

This video from the University of Dayton narrated by Prof. Andrew Murray provides an excellent illustration of the important concept of mechanical advantage.