Bio
From Milton MA and shaped by La Salettes with Shaker roots, Paul did his undergraduate work at Tufts University and his mechanical engineering graduate work (PhD) at Stanford under Thomas Kane.
As a young adult, Paul worked summers landscaping, farming, logging, and construction, then worked at MIT Lincoln Laboratory, NASA Ames, Knowledge Revolution, and MSC.Software, was a consulting editor for McGraw-Hill (mechanics), and has been a consultant for the software, robotics, biotechnology, energy, automotive, and mechanical/aerospace industries.
He helped develop force/motion software used by more than 12 million people worldwide and translated into 11 spoken languages. These software applications include Interactive Physics, Working Model 2D/3D, MSC.visualNastran 4D (now SimWise), NIH Simbody/OpenSim, and the symbolic manipulators Autolev/MotionGenesis.
Paul currently works on Drake, open-source software developed by TRI (Toyota Research Institute) to simulate robots. In his role as Lead TRI/Stanford Liaison for SAIL (Toyota's Center for AI Research at Stanford), he facilitates research between TRI and Stanford.
At Stanford, Paul greatly enjoys working with students and teaches mechanics (physics/engineering), controls/vibrations, and advanced dynamics & computation/simulation. He has written several books on dynamics, computation, and control (broadly adopted by universities and professionals).
Paul is highly appreciative of support from Stanford alumni Dave Baszucki (Roblox CEO). Paul greatly appreciates having worked with Dave and team in developing internationally acclaimed physics, engineering, and educational software, including Interactive Physics, Working Model, and MSC.visualNastran.
He is very grateful to students, co-instructors (TAs), faculty, and staff.
Academic Appointments
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Lecturer, Mechanical Engineering
Administrative Appointments
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Lead TRI/Stanford Liaison, Toyota Research Institute (2018 - Present)
Honors & Awards
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Tau Beta Pi Teaching Honor Roll (one of 12 instructors in school of engineering), Tau Beta Pi (2022)
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Tau Beta Pi Teaching Honor Roll (one of 12 instructors in school of engineering), Tau Beta Pi (2019)
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Tau Beta Pi Teaching Honor Roll (one of 12 instructors in school of engineering), Tau Beta Pi (2018)
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Tau Beta Pi Teaching Honor Roll (one of 12 instructors in school of engineering), Tau Beta Pi (2017)
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Tau Beta Pi Professor of the Year, Tau Beta Pi (2010)
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SOLE Diversity Professor of the Year/Keynote, Stanford Society of Latino Engineers (2007, 2008, 2012, 2017, 2019)
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Co-PI Stanford K-12 Challenge, Stanford (2008)
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Outstanding Achievement in Engineering Practice (mid-career award), Tufts University (2003)
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NDES Best Desktop Software award, MSC Software (1998)
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NASA Tech Briefs Product of the Year, Knowledge Revolution (1998)
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Design News Product of the Year, Knowledge Revolution (1996)
Boards, Advisory Committees, Professional Organizations
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Member, ASME - American Society of Mechanical Engineers (1984 - Present)
2024-25 Courses
- Advanced Dynamics & Computation
ME 331A (Win) - Advanced Dynamics, Simulation & Control
ME 331B (Spr) - Dynamic Systems, Vibrations and Control
ME 161 (Aut) - Mechanical Engineering Teaching Assistance Training
ME 492 (Win) -
Independent Studies (1)
- Ph.D. Teaching Experience
ME 491 (Aut)
- Ph.D. Teaching Experience
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Prior Year Courses
2023-24 Courses
- Advanced Dynamics & Computation
ME 331A (Win) - Advanced Dynamics, Simulation & Control
ME 331B (Spr) - Dynamic Systems, Vibrations and Control
ME 161 (Aut) - Mechanical Engineering Teaching Assistance Training
ME 492 (Win)
2022-23 Courses
- Advanced Dynamics & Computation
ME 331A (Win) - Advanced Dynamics, Simulation & Control
ME 331B (Spr) - Dynamic Systems, Vibrations and Control
ME 161 (Aut) - Vector and Mathematical Analysis for Mechanics
PHYSICS 40 (Aut)
2021-22 Courses
- Advanced Dynamics & Computation
ME 331A (Win) - Advanced Dynamics, Simulation & Control
ME 331B (Spr) - Vector and Mathematical Analysis for Mechanics
PHYSICS 40 (Aut)
- Advanced Dynamics & Computation
All Publications
- Textbook: Dynamics of Mechanical, Aerospace, and Bio/Robotic Systems Prodigy Press. 2024
- Statics & Dynamics: Mechanical, Aerospace, and Bio/robotic Systems, Prodgy Press. 2024
- Textbook: Control, Vibration, and Design of Dynamic Systems Prodigy Press. 2024
- Textbook: Advanced Dynamics and Motion Simulation Prodigy Press. 2024
- SEED: Series Elastic End Effectors in 6D for Visuotactile Tool Use IEEE/RSJ International Conference on Intelligent Robots and Systems arXiv:2111.01376v1. 2022
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A Unified Method for Multi-Body Systems Subject to Stick-Slip Friction and Intermittent Contact
IEEE/RSJ International Conference on Intelligent Robots and Systems
IEEE. 2008: 2311–2316
View details for Web of Science ID 000259998201149
- A Unified Method for Multi-Body Systems Subject to Stick-Slip Friction and Intermittent Contact IEEE/RSJ International Conference on Intelligent Robots and Systems 2008
- Interactive Physics Curriculum Workbook 2008
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A simple method to obtain consistent and clinically meaningful pelvic angles from Euler angles during gait analysis
JOURNAL OF APPLIED BIOMECHANICS
2007; 23 (3): 218-223
Abstract
Clinical gait analysis usually describes joint kinematics using Euler angles, which depend on the sequence of rotation. Studies have shown that pelvic obliquity angles from the traditional tilt-obliquity-rotation (TOR) Euler angle sequence can deviate considerably from clinical expectations and have suggested that a rotation-obliquity-tilt (ROT) Euler angle sequence be used instead. We propose a simple alternate approach in which clinical joint angles are defined and exactly calculated in terms of Euler angles from any rotation sequence. Equations were derived to calculate clinical pelvic elevation, progression, and lean angles from TOR and ROT Euler angles. For the ROT Euler angles, obliquity was exactly the same as the clinical elevation angle, rotation was similar to the clinical progression angle, and tilt was similar to the clinical lean angle. Greater differences were observed for TOR. These results support previous findings that ROT is preferable to TOR for calculating pelvic Euler angles for clinical interpretation. However, we suggest that exact clinical angles can and should be obtained through a few extra calculations as demonstrated in this technical note.
View details for Web of Science ID 000248703000006
View details for PubMedID 18089919
- Theory, Simulation, and Hardware: Lab Design for an Integrated Systems Dynamics Education ASME Mechanical Engineering Congress and Exposition 2005
- A Controversial Study of the Aerodynamics of a Baseball ASME International Conference on Multi-body Systems, Nonlinear Dynamics, and Control 2005
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Inputoutput
MECHANICAL ENGINEERING
2002; 124 (10): 88-88
View details for Web of Science ID 000178360300032
- Constraint Force Algorithm for Formulating Equations of Motion First Asian Conference on Multibody Dynamics 2002
- Efficient Dynamics for Systems Involving Gyrostats Journal of Guidance, Control, and Dynamics 2001; 24 (6): 1144-1156
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In regards to the "ISB recommendations for standardization in the reporting of kinematic data."
Journal of Biomechanics,
1999
View details for DOI 10.1016/s0021-9290(99)00077-9
- Efficient Simulation of Motions Involving Coulomb Friction Journal of Guidance, Control, and Dynamics 1999; 22 (1)
- Efficient Simulation of Motions Involving Coulomb Friction First Symposium on Multibody Dynamics and Vibrations 1997
- Kane’s Checking Function: Modifications and Use in the Integration of Dynamical Equations AIAA Guidance, Navigation, and Controls Conference 1997
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Motion variables leading to efficient equations of motion
INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
1996; 15 (5): 522-532
View details for Web of Science ID A1996VJ83400007
- Unified Computation of Stick-Slide Friction: Application to Rattlebacks, Tops, and Journal Bearings AIAA Guidance, Navigation, and Controls Conference 1995