Innovative Multi-Angle
Rocking Chair Design: The
Stylish Solution to Tiredness
Submitted as a partial requirement
for the course INME4011: Section 156
Design Course for B.S. in Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Students:
Crespo Quiñones, Carlos
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Fabre Ortiz, Norberto
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Flores Lozada, Juan
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Rosado Gracia, Edwin
Undergraduate Student at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
Faculty Advisor:
Vijay K. Goyal, PhD
Professor at Mechanical Engineering Department
University of Puerto Rico at Mayagüez, Mayagüez, PR
May 2005
ii
Project Report
To:
Dr. Vijay K. Goyal
From: Crespo Quiñones, Carlos; Fabre Ortiz, Norberto; Flores Lozada, Juan; Rosado Gracia, Edwin
Date:
May 13, 2005
Re:
Engineering Design Project (INME4011: Section 156)
Dear Prof. Goyal:
Greetings. The purpose of this project is to redesign and improve the looks and functionality of a rocking chair. The chair is
designed for a diversity of uses including relaxation, to have fun, to look good in your home, etc. Enclosed with this letter is a description
of our project.
For our chair, our group wanted a design that would truly change the concept of a rocking chair. Our goal was to take the
rocking chair to the 21st century. With this in mind, our design features a two axis rocking motion which redefines what a rocking chair is.
The chair will be able to rock forward and backwards and also in the lateral directions for a totally new way to sit in a chair. It will be
controlled by four actuators connected to the base and to the main shaft which will always help the chair get to the neutral position.
Although the chair is not intended for small children, or people over 250lb, it ensures a new way to see rocking chairs.
If any of us can be of further help, please do not hesitate to contact us.
Regards,
Carlos Crespo Quiñones
Norberto Fabre Ortiz
Juan Flores Lozada
Edwin Rosado Gracia
iii
Innovative Multi-Angle Rocking Chair Design: The
Stylish Solution to Tiredness
Carlos Crespo Quiñones, Norberto Fabre Ortiz,
Juan Flores Lozada and Edwin Rosado Gracia
Satisfy the need of a futurist, funny, and comfortable rocking chair is the main goal of
this project. For years many rocking chairs have been made with many different mechanisms but
always creating the same motion generation. For the 21st century in addition of a futurist visual
appeal the rocking chair of this project promise to revolutionize the world of rocking chair with a
multi-axial motion generation. With that motion in mind an improved mechanism was designed
to achieve a smooth and safe motion.
This chair was developed for the use of persons with a maximum weight of 300 lb that
creates a bending moment, a torsion and axial load. For every load a diagram was done from
where information was obtained to find the state of stress. A critical point was encountered and
five points were analyzed to find the most critical points, taking out a specific state of stress for
each critical point.
To find the principal stresses the Eigen value approach was used, and Von Mises stress to
find the equivalent stress. Also a static loading analysis with emphasis in the maximum shear
stress criterion and the distortion energy criterion was done, both with the diameter as a variable
to solve. A buckling analysis with an assumed pin-fixed column also was made also using the
diameter as a variable. Finally the diameter was chosen to satisfy and hold all the loads applied.
Complete failure prevention analyses, from fatigue to crack propagation, were performed
to achieve an excellent and safe design. The main shaft is designed to be safe even if a
circumferential surface crack of 0.5 inches is around it. From fatigue it was encountered the
alternating load and the mean load to finally find an equivalent stress. This equivalent stress was
plotted on an S-N diagram and was found that the life of the critical member is to be infinite.
Taking in account all the specifications to make a well designed chair this project
combines all the characteristics from a conventional rocking chair and adds a new way of motion
making the chair more fun to use without leaving that important thing called safety. The visual
appeal and the new motion generated of this rocking chair are looking to next level, to the future,
leaving all the others obsolete.
iv
Acknowledgements
This project and design would have never been possible to realize if we did not had the knowledge
we posses and if a lot of people would not have dedicated a lot of their time and effort, that is why we want
to acknowledge the following:
First we are grateful to the University of Puerto Rico, Mayagüez Campus for providing the
mechanical engineering bachelor degree program and giving us the opportunity to study and to become
engineers.
We also like to thank all the professors for dedicating their time to give us their knowledge and to
teach us the basic of the principles and laws that we applied on this design.
But especially we want to thank Dr. Goyal for teaching us how to use that knowledge, for teaching
us how we can use all that we already have learned to design and built new things and most important of all
for preparing us for the real working world.
v
List of Contents
List of Figures ……………………………………………………………………vii
List of Tables ………………………………………………………………………x
Chapter 1. Preliminary Remarks ………………………………………...…....……..1
1.1 Background …………………………………………..………....…...…1
1.2 Literature Survey ……..………………………………..………….……3
1.3 Problem Description ……………………..…………..……….…...……3
1.4 Expected Outcomes …………………….……………..………….……4
Chapter 2. Project Description ……………………………………………....…..…..5
2.1 Description of the Project ……………..………..……..………..…….…5
2.2 Design Selection …..…………………..………..……..…….……….…5
2.2.1
First Idea …………………..…………………..…...……….…6
2.2.2
Second Idea ….……………..……………..…..…………….…6
2.2.3
Selected Design ……………..……………..…..…....……….…7
2.3 Methodology …..……….……………..………..……..…………….…8
2.4 Material Selection …...……………..………..……..…………….….…8
Chapter 3. Stress Analysis ………..…………………..…………..………....…..…..10
3.1 Assembly ……………………………………..……..…..………….…10
3.2 Dynamic Analysis ……………..…………………..…..…………….…12
3.3 Stress Analysis ……….…………..……………..……..…………….…14
3.3.1
Free Body Diagram ……..……………..…….…...………….…15
3.3.2
Normal Stresses ……..……………..…….……..……..…….…18
3.3.3
Shear Stresses ……..……………..…….…………..….…….…20
3.3.4
State of Stress at Critical Point ………..…….……………….…22
vi
3.3.5
Principal Stresses ……..……………..…….………..……….…24
3.3.6
Von Mises Stress ……..……………..….…….……….…….…28
3.4 Discussion…………….……………..……………………..…….….…28
Chapter 4. Failure Analysis ……………………………...………..…….......…..…..29
4.1 Static Theories of Failure ……………………...……..…..…….…….…29
4.2 Fracture …………..…………………………..…………………..….…31
4.3 Stability ……………..…..……………………………………….….…34
4.4 Fatigue ……………………………………....…..………………….…35
4.5 Discussion …………………………….....………………………….…37
Chapter 5. Results and Discussion ……………..………………………………..…..39
5.1 Present Design …………….………….………..……..…..………….…39
5.2 Discussion ……………………………………..……..…..………….…40
5.3 Cost Analysis …………………...…………………..……………….…41
Chapter 6. Final Remarks ………………………………..……………………..…..42
6.1 Conclusion ……………………………..……..……..…..………….…42
6.2 Recommendations …………..…….………………..……………….…43
References ……………………………………………………………………..…..44
Appendix …………………………………………………..…………………..…..45
A. Submitted Proposal ……………………….…..……..…..………….…45
B.
Engineering Drawings…………………………………....………….…54
C. Analysis & Calculations …………………………..………………….…60
D. Complementary Information ……………………..……….………….…82
Student Vitae ..……………………………………………...…………………..…..87
vii
List of Figures
Figure 1.1: Yorkshire rocking chair ……………………………………………………….…………2
Figure 1.2: Ron rocking chair ………………………………………………………….…………….2
Figure: 2.2.2.1: Second idea for the rocking chair design ……………………………………….6
Figure: 2.2.3.1: Third idea and selected design ……………………………………………….....7
Figure 3.1.1: Main Shaft ………………………………………………………………..………10
Figure 3.1.2: Actuator ………………………………………………………………….……….10
Figure 3.1.3: Rotating Pins ……………………………………………………………………..11
Figure 3.1.4: Chair Base ……………………………………………………………………………11
Figure 3.1.5: Seating Section …………………………………………………………...………11
Figure 3.1.6: Final Assembly of the Rocking Chair .
…………………………………………….…………..12
Figure 3.2.1: Inverted slider crack mechanism
………………………………………………….……….…..12
Figure 3.2.2: Length of the actuator in relation to the main shaft’s angle ..………………………..…….13
Figure 3.2.3: Elongation velocity of the actuator in relation to the main shaft’s angle …………....……....14
Figure 3.3.1: The position of the main shaft at its inclined position ………………….………...…..…15
Figure 3.3.2: Main shaft and actuators position on the inclined position …………..………..….……..……16
Figure 3.3.3: Main shaft and actuators position on the neutral position ……………………………....……16
Figure 3.3.4: Free Body Diagram (FBD) for the main shaft at the inclined position ..…………17
Figure 3.3.5: Free Body Diagram (FBD) for the main shaft at the neutral position …...………18
Figure 3.3.2.1: Shaft at inclined position with corresponding axial load vectors ………………19
Figure 3.3.2.2: Normal stress diagram for the main shaft at the inclined position …………………19
viii
Figure 3.3.3.1: Shaft at inclined position with corresponding shear load vectors ………...……20
Figure 3.3.3.2: Shear Load diagram for the main shaft at the inclined position ……………………………21
Figure 3.3.3.3: Bending Moment Diagram for the main shaft at the inclined position …………….……….22
Figure 3.3.4.1: Axial moment (Torque) diagram for the main shaft at the inclined position …………...…...23
Figure 3.3.5.1: Critical cross-section ……………………………………………………......…...……….24
Figure 4.2.1: Disk fracture and loads present at the critical cross-section …………………….....…..……...32
Figure 4.3.1: Main shaft at neutral position under a buckling load …………...………..……………..……34
Figure 4.4.1: Applied Fully-Reversed Bending Moment on the main shaft ……...….………...….….…….36
Figure 4.4.2: Alternating Stress diagram for the main shaft ……...……………….……..…….....................36
Figure 4.4.3: Mean Stress diagram for the main shaft ……...………….………..……...…...………..……36
Figure 4.4.4: S-N Diagram for the main shaft under fluctuating multi-axial stresses ........……………….…37
Figure 5.5.1: Overall View of the Chair ………….……….……...……………………………....………39
Figure A.C.2.1: Shaft at inclined position with corresponding axial load vectors ……...…….…61
Figure A.C.2.2: Axial loads for section I ……...……………….……….……...…………….…..…61
Figure A.C.2.3: Axial loads for section II ……...……………….……….……...……………….…62
Figure A.C.3.1: Shaft at inclined position with corresponding shear load vectors ………….…63
Figure A.C.3.2: Shear and bending moments for section I……………………………………..63
Figure A.C.3.3: Shear and bending moments for section II ……………………………………64
Figure A.D.1: Gungstol with 6 legs …………………………………………………………….82
Figure A.D.2: shaker rocking chair, cherry construction with woven tape seat ……………..…82
Figure A.D.3: Static Base Rocking Chair ....…………………………………………………...83
Figure A.D.4: 'Egg' rocking chair manufactured by Antonio Volpe …………………………...83
Figure A.D.5: Model nr. B306 (1928) design by Pierre Jeanneret and Charlotte Perriand ……83
Figure A.D.6: Rattan high back swivel rocking chair ………………………………………….84
Figure A.D.7: 'PS 16', 'rocking chaise by Franco Albini ……………………………………….84
ix
Figure A.D.8: 'Pastil' rocking armchair by Eero Aarnio ……………………………………….84
Figure A.D.9: 'Easy edges', rocking chair by Frank O. Gehry …………………………………85
Figure A.D.10: 'Gravity balance' rocking chair by Peter Opsvik ………………………………85
Figure A.D.11: Spring rocker ………………………………………………………………......85
x
List of Tables
Table 2.2.4.1: Design Selection using Pugh’s Method …………………………………………7
Table 2.4.1: Material Selection using Pugh’s Method …………………………………….……9
Table 4.1: Design criteria ratings for overall significance on the design safety factor …….......29
Table 4.2: Obtained Values for the Main Shaft using the DEC and MSSC ……………………31
Table 4.4.1: Results for the fatigue analysis for the main shaft ……………………………..…35
Table 5.3.1: Cost Analysis …………………………………………………………………...…41