Rectilinear Six-bar

Rectilinear Six-Bar (Candy Coating Linkage)

Jeff Glabe designed this six-bar linkage to move through six task positions while maintaining a parallel orientation.  This required the calculation of 55,000 linkages to find 26 that work.  This one has the additional feature that it is operated by a rotating crank (the red link).  The video is a collaboration of Jeff Glabe and Benjamin Liu.

 

Intro KSM

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
chapter3-4

Superluminal Chapter 4

David finds that surpassing Siggy and Kwan to get to Satellite 9 may have benefits he did not expect. 

 

 

Superluminal Chapter 4
Chapter 1 Busted

Superluminal Chapter 3

More of R. W. Frost’s story following David Minor’s uneasy relationship with MitsukoTek Corporation as he is drawn into helping their wayward Satellite 9.

(Read by scrolling the image or by using the page down and up buttons at the bottom.)

Superluminal Classic 1012 C3
Hummingbird Spatial Six-bar

Hummingbird Spatial Six-bar Linkage

This spatial six-bar linkage provides a compact flapping wing mechanism for a hovering micro air vehicle that controls both swing and pitch movements.  It is the result of a collaboration between Benjamin Liu and Peter Wang.

 

cover_sample

Superluminal Chapters 1-2

Superluminal, the new book by R. W. Frost, follows David Minor’s experiences with MitsukoTek Corporation’s troublesome Satellite 9.  It is the year 2035 and a new technology has swept the globe…

(Read by scrolling the image or by using the page down and up buttons at the bottom.)

Superluminal Chapter 1-2
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