Point configurations that are asymmetric yet balanced

A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in R^3, and his classification is equivalent to the converse for R^3. In this paper we disprove the converse in high dimensions. We construct several counterexamples, including one with trivial symmetry group.Comment: 10 page

Physical demand but not dexterity is associated with motor flexibility during rapid reaching in healthy young adults

Healthy humans are able to place light and heavy objects in small and large target locations with remarkable accuracy. Here we examine how dexterity demand and physical demand affect flexibility in joint coordination and end-effector kinematics when healthy young adults perform an upper extremity reaching task. We manipulated dexterity demand by changing target size and physical demand by increasing external resistance to reaching. Uncontrolled manifold analysis was used to decompose variability in joint coordination patterns into variability stabilizing the end-effector and variability de-stabilizing the end-effector during reaching. Our results demonstrate a proportional increase in stabilizing and de-stabilizing variability without a change in the ratio of the two variability components as physical demands increase. We interpret this finding in the context of previous studies showing that sensorimotor noise increases with increasing physical demands. We propose that the larger de-stabilizing variability as a function of physical demand originated from larger sensorimotor noise in the neuromuscular system. The larger stabilizing variability with larger physical demands is a strategy employed by the neuromuscular system to counter the de-stabilizing variability so that performance stability is maintained. Our findings have practical implications for improving the effectiveness of movement therapy in a wide range of patient groups, maintaining upper extremity function in old adults, and for maximizing athletic performance

Novel Optimised Structural Aluminium Cross-Sections Towards 3D Printing

In the last decades, the deployment of aluminium and its alloys in engineering fields has been increased significantly, due to the material’s special features accompanied by supportive technological and industrial development such as the extrusion manufacturing method. However, the extent of aluminium structural applications in building activities is still rather limited, and barriers related to strength and stability issues prevent its wider use. In the context of topology optimisation, appropriate design in aluminium cross-sections can overcome inherent deficiencies, such as the material’s low elastic modulus. The current study investigates the application of structural topology optimisation to the design of aluminium beam and column cross-sections, through a combination of 2D and 3D approaches, with focus on post-processing and manufacturability. Ten unique cross-sectional profiles are proposed based on structural testing through Finite Element Analysis (FEA). Conclusions attempt to highlight the general characteristics of the optimised aluminium cross-sections as well as the benefits of the using extrusion and 3D printed manufacturing methods in order to realise these results