Adrian Bowyer

Biomimetics: its practice and theory

Biomimetics, a name coined by Otto Schmitt in the 1950s for the transfer of ideas and analogues from biology to technology, has produced some significant and successful devices and concepts in the past 50 years, but is still empirical. We show that TRIZ, the Russian system of problem solving, can be adapted to illuminate and manipulate this process of transfer. Analysis using TRIZ shows that there is only 12% similarity between biology and technology in the principles which solutions to problems illustrate, and while technology solves problems largely by manipulating usage of energy, biology uses information and structure, two factors largely ignored by technology.

Reprap ??? the replicating rapid prototyper

This paper presents the results to date of the RepRap project ??? an ongoing project that has made and distributed freely a replicating rapid prototyper. We give the background reasoning that led to the invention of the machine, the selection of the processes that we and others have used to implement it, the designs of key parts of the machine and how these have evolved from their initial concepts and experiments, and estimates of the machines reproductive success out in the world up to the time of writing (about 4500 machines in two and a half years).

Comparison of interval methods for plotting algebraic curves

This paper compares the performance and efficiency of different function range interval methods for plotting f(x, y)=0 on a rectangular region based on a subdivision scheme, where f(x, y) is a polynomial. The solution of this problem has many applications in CAGD. The methods considered are interval arithmetic methods (using the power basis, Bernstein basis, Homer form and centred form), an affine arithmetic method, a Bernstein coefficient method, Taubins method, Rivlins method, Gopalsamys method, and related methods which also take into account derivative information. Our experimental results show that the affine arithmetic method, interval arithmetic using the centred form, the Bernstein coefficient method, Taubins method, Rivlins method, and their related derivative methods have similar performance, and generally they are more accurate and efficient than Gopalsamys method and interval arithmetic using the power basis, the Bernstein basis, and Horner form methods.

Voronoi diagrams of set-theoretic solid models

The definition of a Voronoi diagram is extended to arbitrary set-theoretic solid models. A method for approximating such diagrams using recursive subdivision is described. The method relies on octrees, which have been used for computing the distances between whole solid models. Two- and three-dimensional images generated using the algorithm are presented.<<ETX>>

Take-off and landing forces and the evolution of controlled gliding in northern flying squirrels Glaucomys sabrinus.

SUMMARY Flying squirrels are well known for their ability to glide between trees at the top of a forest canopy. We present experimental performance and behavioural evidence that flight in flying squirrels may have evolved out of a need to control landing forces. Northern flying squirrels were filmed jumping from a horizontal branch to a much larger vertical pole. These were both slightly compliant (less than 1.9 mm N–1), and instrumented using strain gauges so that forces could be measured. Take-off and landing forces were both positively correlated with horizontal range between 0.5 and 2.5 m (r=0.355 and r=0.811, respectively, P<0.05), but not significantly different to each other at each range tested. Take-off forces ranged from 1 to 10 bodyweights, and landing forces were between 3 and 10 bodyweights. Glide angles increased rapidly with horizontal range, approaching 45° at 3 m, above which they gradually decreased, suggesting that northern flying squirrels are optimised for long distance travel. We show that northern flying squirrels initiate full gliding posture at ranges of less than 1 m, without landing any higher than an equivalent ballistic projectile. However, this gliding posture enables them to pitch upwards, potentially stalling the wing, and spreads the landing reaction force over all four extended limbs. At steeper approach angles of close to 45°, flying squirrels were unable to pitch up sufficiently and landed forelimbs first, consequently sustaining higher impact forces. We investigate four hypotheses to explain the origin of flight in these animals and conclude that the need to reduce landing impact forces was most likely to have stimulated the development of aerial control in flying squirrels.

Robust arithmetic for multivariate Bernstein-form polynomials

Abstract There are several ways to represent, to handle and to display curved surfaces in computer-aided geometric design that involve the use of polynomials. This paper deals with polynomials in the Bernstein form. Other work has shown that these polynomials are more numerically stable and robust than power-form polynomials. However, these advantages are lost if conversions to and from the customary power form are made. To avoid this, algebraic manipulations have to be done in the Bernstein basis. Farouki and Rajan (R.T. Farouki, V.T. Rajan, Algorithms for polynomials in Bernstein form, Computer Aided Geometric Design 5 (1988) 1–26) present methods for doing arithmetic on univariate Bernstein-basis polynomials. This paper extends all polynomial arithmetic operations to multivariate Bernstein-form polynomials.

A Survey of Global Configuration-Space Mapping Techniques for a Single Robot in a Static Environment

The mapping from workspace to configuration space (C-space) plays a major role in the field of kinematics, with applications including robotics path planning, packing and nesting, automated assembly, and mechanism analysis. Over the past 20 years, research into the problem has resulted in many techniques that can be combined to suit a specific application. This survey aims to provide the developer of a C-space-based system with an overview of those techniques that map the global C-space of a single robot in a static environment. We discuss issues concerning how the robot and its environment are modeled (including how approximations can be used to make C-space mapping easier) and describe a range of schemes used to represent a C-space map. We then discuss the key techniques used to generate a C-space map for mobile robots and manipulators. The survey of literature is summarized by tables that list some 50 individual mapmaking papers, classifying each according to criteria identified in earlier sections. Finally, we draw conclusions from the findings of the survey. Note that, although reference is made throughout to robots, the controlled objects may equivalently be components or assemblies. In particular, results for mobile robots are fundamental to all C-space mapmaking problems.

CSG set-theoretic solid modelling and NC machining of blend surfaces

This paper presents a new solid modelling system capable of representing three dimensional objects consisting of both simple and complicated surfaces and, equally importantly, blend surfaces between them. Implicit polynomial inequalities and set theoretic techniques are used to specify the models. The modelling system can generate shaded pictures and NC machining instructions for cutting complicated objects automatically. The modelling system uses a technique for generating polynomials for blends and fillets that allows the user complete control over their extent without requiring him or her explicitly to devise the polynomial inequalities needed to represent them.

Multidimensional set-theoretic feature recognition

A new method of feature recognition in set-theoretic geometric modelling is proposed which allows its users complete control over the geometrical definition of form features. The method looks for instances where one set-theoretic model under multidimensional transformations coincides with all of, or part of, another. The attributes of the possible match locations are then reported back to the user. The method also permits the implementation of a tolerance level which allows matches whose goodness of fit is below this level to be ignored. All possible instances of features whose exact geometries are unknown can be defined parametrically. The method reports back the parameter values of match positions along with the other match attributes. The method also has applications to the nesting and docking problems.

Interval methods in geometric modeling

This paper is about using interval computations in location, simplification, and root-finding for multivariate implicit functions that are used as shape primitives in a set-theoretic (that is, a CSG) geometric modeller. Three problems are discussed, and solutions to them presented: the location and simplification of the surfaces of semialgebraic sets (surfaces involving some transcendental functions are dealt with as well); the generalization of Newton-Raphson using intervals; and interval ray-tracing. Examples are presented for both conventional three-dimensional geometric models and for CSG models in higher dimensions representing configuration-space maps for moving and colliding three-dimensional objects.