Peter Donelan


Teaching in 2018

Research interests

Singularity theory, geometry, applications to robotics, robot manipulators and mechanisms


BSc Hons (Bristol), PhD (Southampton)

About me

My PhD explored the singularity theory of motions of a rigid body.  I discovered important applications in mathematical robotics and learned that there is a wide range of problems there involving interesting geometry.  That has led me into research involving algebraic geometry, especially the theory of invariants and Gröbner bases, differential geometry and Lie groups .  I have developed graduate courses in all these topics.  I enjoy teaching undergraduate calculus and differential equations.

As Head of School, I aim to ensure students have the best possible education in the mathematical sciences, whether they enjoy the theoretical and abstract aspects or understanding how they can be used to solve problems in so many other fields.  Both of these make mathematics and statistics students among the most sought after graduates in employment.  The development of new programmes in actuarial science, applied statistics and data science, close links with engineering and computer science and strong connections with schools and secondary teachers are some aspects of our current development, while maintaining the school’s reputation as one of the leading research units attracting funding both in New Zealand and internationally is fundamental to our place in the university.


I am currently working on problems in singularities of robot kinematics, invariant theory and the classification of mechanisms, pseudoinverses for non-Riemannian metrics, kinematics of geared mechanisms, while a recent PhD student’s thesis on mathematics and poetry has led to research on the Romanian mathematician/poet Barbilian.

Supervision interest

I will supervise postgraduate projects in singularity theory, especially with application to kinematics, and other aspects of the geometry of motion using techniques of algebraic geometry and Lie theory.

Current Master and PhD students

Seyedvahid Amirinezhad (PhD): Kinematic Singularities of Geared Mechanisms

Past Master and PhD students

Loveday Kempthorne (PhD joint with Translation Studies): Relations between Modern mathematics and Poetry: Czeslaw Milosz; Zbigniew Herbert; Ion Barbu/Dan Barbilian

Mohammed Daher (PhD): Dual Numbers and Invariant Theory of the Euclidean Group with Applications to Robotics

Amani Ahmed Otaif (MSc): Constraint Equations for a Planar parallel Platform

Deborah Crook (MSc): Polynomial Invariants of the Euclidean Group Action on Multiple Screws

Sandra Chapman (MSc): The Geometry of the Point-Path Generated by Rigid Body Motion in Two and Three Dimensions

Christopher Scott (MSc): Real Inflexions of the Four-Bar Coupler Curve

List of selected publications

M. Daher and P. Donelan, Invariants of the k-fold adjoint action of the Euclidean isometry group, J. Geometry, (2015) ( 17pp

M. Daher and P. Donelan, Invariant properties of the Denavit-Hartenberg parameters, in Interdisciplinary Applications of Kinematics, Mechanisms and Machine Science Vol. 26, eds A. Kecskemethy and F. Geu Flores, Springer (2015) 43-51

P. Donelan and A. Müller, General formulation of the singularity locus for a 3-dof regional manipulator, in Proc. Int. Conf. Robotics and Automation, Shanghai, 2011, IEEE, Piscataway NJ, (2011) 3958-3963

P. Donelan and A. Müller, Singularities of regional manipulators revisited, in Advances in Robot Kinematics, Portoroz, 2010, eds J. Lenarcic and M. Stanisic, Springer, Dordrecht (2010)  509-519

P. S. Donelan, Kinematic singularities of robot manipulators, in Advances in Robot Manipulators, ed A. Lazinica, In-Tech, Vienna, Austria (2010) 401-416

P. Donelan, Genericity conditions for serial manipulators, in Advances in Robot Kinematics, Batz-sur-Mer, 2008, eds J. Lenarcic and P. Wenger, Springer, Dordrecht (2008) 185-192

J. M. Selig and P. Donelan, A screw syzygy with application to robot singularity computation, in Advances in Robot Kinematics, Batz-sur-Mer, 2008, eds J. Lenarcic and P. Wenger, Springer, Dordrecht (2008) 147-154

P. S. Donelan, Singularity-theoretic methods in robot kinematics, Robotica, 25 (2007) 641-659

P. S. Donelan,  Singularities of robot manipulators, in Singularity Theory, Proc. 2005 Marseille Singularity School and Conference, eds D. Cheniot et al, World Scientific, Singapore (2007) 189-218

J.-P. Merlet and P. Donelan,  On the regularity of the inverse Jacobian of parallel robots, in Advances in Robot Kinematics, Ljubljana, 2006, eds J. Lenarcic and B. Roth, Springer, Dordrecht (2006) 41-48

M. Cocke, P. S. Donelan and C. G. Gibson, Trajectory singularities for a class of parallel motions, in Real and Complex Singularities, Sao Carlos Workshop, Marseille, 2004, eds J.-P. Brasselet and M. A. Soares Ruas, Birkhauser (2006) 53-70

M. Cocke, P. S. Donelan and C. G. Gibson, Instantaneous singular sets associated to spatial motions,  in Real and Complex Singularities, Sao Carlos Workshop, 1998, eds. F. Tari and J. W. Bruce, Res. Notes Math., 412 Chapman and Hall/CRC, Boca Raton, (2000) 147-163

P. S. Donelan and C. G. Gibson, Singular phenomena in kinematics, in Singularity Theory, Proc. European Singularities Conf., Liverpool, 1996,  London Math. Soc. Lecture Notes 263, Cambridge UP (1999) 379-402

P. S. Donelan, C. G. Gibson and  W. Hawes, Trajectory singularities of general planar motions, Proc. Royal Soc. Edinburgh, 129A (1999) 37-55

P. S. Donelan and C. P. Scott, Real inflections of four-bar coupler curves, Mechanism and Machine Theory, 30 (1995) 1179-1191

P. S. Donelan and C. G. Gibson, On the hierarchy of screw systems, Acta Applicandae Mathematicae, 32 (1993) 267-296


Teaching in 2018