Mechanism Design

I was the "Machines and Mechanisms II" course (MAE412/512) Teaching Assistant for several years (2003-2007), when my thesis advisor, Dr Krovi, is teaching the course. Throughout these years, I developed lecture notes/ simulations/ Code to assist student in understanding the course materials.

Here are some of the mechanism simulations that I created for the class to help student understanding / visualize how a mechanism works. For more videos, please visit my YouTube page at: YouTube.

Video Collections:

One-link

One link Mechanism Simulation. - Homework 01 solution for Fall 2007 MAE412/512 Machines and Mechanism II class. - Given theta(t)=cos(t), and r(t)=3+2sin(t) as t: 0 - 10sec, calculate the x, y position of the end-effector (the tip) of the one-link mechanism.

Dynamic Simulation of a Compound Pendulum. - Dynamic Simulation of a Pendulum using MATLAB. In this simulation, there is no friction or torsional spring attached to the joint (will add these in subsequent simulations and see the effects). - Simulation time is 10 sec and solve using MATLAB ode45. - Parameters used in this simulation: m=5, Mass of the pendulum; g=9.81, Gravitational Acceleration; a=2, Length from joint to C.M.; L=2*a, Total length of the pendulum; I=(1/3)*(m*(L)^2), Moment of Inertia.

Four-bar

Four-bar Crank-Rocker Mechanism Simulation. - Simulation with Crossed Configuration. - This is the solution for Homework 02, Problem 2b. - Created for 2007 MAE412/512 Machines and Mechanism II class at SUNY-Buffalo.

Four-bar Crank-Rocker Mechanism Simulation. - Simulation with Uncsrossed Configuration. - This is the solution for Homework 02, Problem 2b. - Created for 2007 MAE412/512 Machines and Mechanism II class at SUNY-Buffalo.

Four-bar Mechanism Simulation. - A MATLAB Simulation of a four-bar mechanism showing the path of a point on the coupler link. - 2007 Homework 05, Problem 2(f) Solution. - This is a Homework solution for MAE412/512 Machines & Mechanisms II class.

Fourbar Mechanism (Crank-Rocker) Simulation. (1 of 2) - Simulation of a four-bar crank-rocker mechanism. As the crank go through a 360 degree rotation, the limiting positions of the rocker is shown. - A singular position also shown as the crank, coupler, and rocker all in a straight line. Shown in solid line is the crossed configuration and dotted line shows the un-crossed configuration.

Fourbar Mechanism (Crank-Rocker) Simulation. (2 of 2) - Simulation of a four-bar crank-rocker mechanism. As the crank go through a 360 degree rotation, the limiting positions of the rocker is shown. - A singular position also shown as the crank, coupler, and rocker all in a straight line. Shown in solid line is the un-crossed configuration and dotted line shows the crossed configuration.

Slider-crank

Slider-Crank Mechanism Simulation - Simulation of a four-bar slider-crank mechanism. As the crank go through a 360 degree rotation, the limiting positions of the slider (r1 value) is shown. - A simulation created for Machines and Mechanism II course where I am the Teaching Assistant.

Limiting Position

Here shown the limiting positions of four-bar mechanism and slider-crank mechanism.

Four-bar

Case I: Crank-Rocker Mechanism.

Fourbar: Crank-Rocker. (1 of 2) - Simulation of a crank-rocker four-bar mechanism to show the limiting position (angle) of the rocker (output link). This is the mechanism at the 'Uncrossed Configuration'. - For Crank-Rocker Mechanism, there is no limiting position for the crank, but there is a limit to the rocker.

Fourbar: Crank-Rocker. (2 of 2) - Simulation of a crank-rocker four-bar mechanism to show the limiting position (angle) of the rocker (output link). This is the mechanism at the 'Crossed Configuration'. - For Crank-Rocker Mechanism, there is no limiting position for the crank, but there is a limit to the rocker.

Fourbar: Double-Rocker. (1 of 4) - Simulation of a double-rocker four-bar mechanism to show the limiting position (angle) of both the rocker (input & output link). - This simulation show the mechanism of the 'crossed configuration' for the motion limit of input link (link 2).

Case II: Rocker-Crank Mechanism.

Fourbar: Rocker-Crank. (1 of 2) - Simulation of a rocker-crank four-bar mechanism to show the limiting position (angle) of the rocker (output linkis r2). This is the mechanism at the 'Uncrossed Configuration'. - For Rocker-Crank Mechanism, there is no limiting position for the crank, but there is a limit to the rocker.

Fourbar: Crank-Rocker. (2 of 2) - Simulation of a rocker-crank four-bar mechanism to show the limiting position (angle) of the rocker (output linkis r2). This is the mechanism at the 'Crossed Configuration'. - For Crank-Rocker Mechanism, there is no limiting position for the crank, but there is a limit to the rocker.

Case III: Double-Rocker Mechanism.

Fourbar: Double-Rocker. (1 of 4) - Simulation of a double-rocker four-bar mechanism to show the limiting position (angle) of both the rocker (input & output link). - This simulation show the mechanism of the 'crossed configuration' for the motion limit of input link (link 2).

Fourbar: Double-Rocker. (2 of 4) - Simulation of a double-rocker four-bar mechanism to show the limiting position (angle) of both the rocker (input & output link). - This simulation show the mechanism of the 'Uncrossed configuration' for the motion limit of input link (link 2).

Fourbar: Double-Rocker. (3 of 4) - Simulation of a double-rocker four-bar mechanism to show the limiting position (angle) of both the rocker (input & output link). - This simulation show the mechanism of the 'Uncrossed configuration' for the motion limit of output link (link 4).

Fourbar: Double-Rocker. (4 of 4) - Simulation of a double-rocker four-bar mechanism to show the limiting position (angle) of both the rocker (input & output link). - This simulation show the mechanism of the 'Crossed configuration' for the motion limit of output link (link 4).

Fourbar: Double-Rocker. (1 of 2) - Simulation of a double-rocker four-bar mechanism to show the limiting position (angle) of both the rocker (input & output link). - This simulation show the mechanism of both the 'Crossed' and 'Uncrossed' configuration for the motion limit of output link (link 4).

Fourbar: Double-Rocker. (2 of 2) - Simulation of a double-rocker four-bar mechanism to show the limiting position (angle) of both the rocker (input & output link). - This simulation show the mechanism of both the 'Crossed' and 'Uncrossed' configuration for the motion limit of input link (link 2).

Slider-Crank

Case I: Crank can fully rotate.

Slider-Crank Mechanism. (1 of 2) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) can rotate 360 degree. - This simulation show the mechanism at the 'Right Branch' configuration.

Slider-Crank Mechanism. (2 of 2) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) can rotate 360 degree. - This simulation show the mechanism at the 'Left Branch' configuration.

Case II: Crank cannot fully rotate.

Slider-Crank Mechanism. (1 of 4) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) cannot rotate 360 degree. - This simulation show the mechanism at the 'Left Branch', 'Uncrossed' configuration.

Slider-Crank Mechanism. (2 of 4) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) cannot rotate 360 degree. - This simulation show the mechanism at the 'Right Branch', 'crossed' configuration.

Slider-Crank Mechanism. (3 of 4) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) cannot rotate 360 degree. - This simulation show the mechanism at the 'Left Branch', 'Crossed' configuration.

Slider-Crank Mechanism. (4 of 4) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) cannot rotate 360 degree. - This simulation show the mechanism at the 'Left Branch', 'uncrossed' configuration.

Slider-Crank Mechanism. (1 of 2) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) cannot rotate 360 degree. - This simulation show the mechanism from the 'Right Branch', 'Uncrossed' configuration to the limit of 'Left Branch', 'Crossed' configuration. Then, it move to the right limit of 'Right Branch' in 'Crossed' configuration.

Slider-Crank Mechanism. (2 of 2) - Simulation of a slider-crank mechanism to show the limiting position (length of travel) of the slider, given the crank (input link) cannot rotate 360 degree. - This simulation show the mechanism move from the limit of 'Right Branch', 'Crossed' configuration, to the limit of 'Left Branch'. Then, it move to the limit of 'Right Branch' in 'Uncrossed' configuration.

Six-bar

Kinematic Simulation of a Six-bar mechanism. ver 1.0. - A homework solution for Fall 2007 MAE412/512 Machines and Mechanism II class (Partial solution for Homework 04 Problem 1). - This one capture at 30fps, for a slower version - 8fps, please look at v2.0 of the same simulation

Kinematic Simulation of a Six-bar mechanism. ver 2.0. - A homework solution for Fall 2007 MAE412/512 Machines and Mechanism II class (Partial solution for Homework 04 Problem 1). - v1.0 record at 30fps, seems a bit too fast, this one capture at 8fps.

Synthesis

One link Mechanism Synthesis (2 points) - Determine the parameters of a one-link mechanism that passes through 2 points with specified angle (delta alpha) between the two points. - Homework #06 Problem 2 Solution for MAE412/512 Machines & Mechanism II class

One Link Mechanism Synthesis (3 points) - Synthesize a one-link mechanism (x,y) and radius R that will pass through three predefine points. - Solution for Homework #06 Problem #1 of MAE412/512 Machines and Mechanism II class.

Fourbar 3 Precision Points Synthesis Solution. (1 of 2) - The resulting fourbar mechanism from a dyadic synthesis. Using the arbitrary free choices we used in the synthesis process, the resulting fourbar mechanism is a crank-rocker (Non-Grashof). - This example demonstrate that with this dyadic synthesis method, there is no guarantee on the type of mechanism (Grashof or Non-Grashof) you will get. There is also no guarantee that the mechanism will pass through all 3 points in one configuration (crossed/ uncrossed).

Fourbar 3 Precision Points Synthesis Solution. (2 of 2) - The resulting fourbar mechanism from a dyadic synthesis. The task is to synthesize a fourbar mechanism that will pass through three precision points using dyadic synthesis method. - This example demonstrate that with this dyadic synthesis method, there is no guarantee on the type of mechanism (Grashof or Non-Grashof) you will get. There is also no guarantee that the mechanism will pass through all 3 points in one configuration (crossed/ uncrossed).

Fourbar 3 Precision Points Synthesis, Fixed Pivot. (1 of 2) - The resulting fourbar mechanism from a dyadic synthesis. The task is to synthesize a fourbar mechanism that will pass through three precision points using dyadic synthesis method. - In addition, we want to fix the pivoting location of the fourbar mechanism at (-15,-10) & (5,-10). The three points are P1(30,5), P2(15,15), P3(5,30). The resulting fourbar mechanism is a crank-rocker.

Fourbar 3 Precision Points Synthesis, Fixed Pivot. (2 of 2) - The resulting fourbar mechanism from a dyadic synthesis. The task is to synthesize a fourbar mechanism that will pass through three precision points using dyadic synthesis method. - In addition, we want to fix the pivoting location of the fourbar mechanism at (-15,-10) & (5,-10). The three points are P1(30,5), P2(15,15), P3(5,30). The resulting fourbar mechanism is a crank-rocker.

Others

Simulation of Theo Jansen Mechanism - The Theo Jansen Mechanism is simply a genius combination of a Four-bar mechanism (Crank-Rocker) with a another four-bar mechanism (use a four-bar with equivalent length here) that create a motion similar to gait motion at the end-effector.

Theo Jansen Mechanism Kinematic Analysis - The Theo Jansen Mechanism is simply a genius combination of a Four-bar mechanism (Crank-Rocker) with a another four-bar mechanism (use a four-bar with equivalent length here) that create a motion similar to gait motion at the end-effector. - In this video shows the kinematic analysis (position, velocity, and acceleration) of the end effector when the input link rotate at a constant velocity of 5 deg/sec (No acceleration).

Tutorial

Tutorial to create a simple MATLAB one-link simulation - The tutorial is written in 2006 for MAE412/512 recitation, I just upload this since I received many 'how to simulate mechanism in MATLAB?' email requests. The resulting animation is shown at left. - It is pretty simple, but it will get you started. Download tutorial: PDF. - For the fourbar analysis part, I recommend the book "Kinematics, Dynamics, and Design of Machinery" by Dr. Waldron Kinzel. - Feel free to send me email if you have any comments on the tutorial.

Note: If you find this tutorial useful, you can consider donate to motivate or just cheer me up with paypal. :)

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Last update: 22 December 2007.