The bouncing ball and the Grünwald-Letnikov definition of fractional derivative

This paper proposes a conceptual experiment embedding the model of a bouncing ball and the Grünwald-Letnikov (GL) formulation for derivative of fractional order. The impacts of the ball with the surface are modeled by means of a restitution coefficient related to the coefficients of the GL fractional derivative. The results are straightforward to interpret under the light of the classical physics. The mechanical experiment leads to a physical perspective and allows a straightforward visualization. This strategy provides not only a motivational introduction to students of the fractional calculus, but also triggers possible discussion with regard to the use of fractional models in mechanics.

Visualization and Quantification of Stresses at the Ends of Short Fibers Embedded in Epoxy Resin

The photoelastic effect was used to visualize and quantify stresses at the end of fibers embedded in birefringent epoxy resin. A method was proposed allowing not to only quantify the differences in main principal stress for a single loading state, but to allow monitoring the evolution of local stress throughout the micro-mechanical experiment. It was found that the ends of fibers foster the formation of shear stresses which influence the principal stress distribution. Typically, star-shaped principal stress distributions were found at the ends of fibers. Finite Element simulations of the tests were in good agreement with the experimental evidence.

Biomechanical design analysis and experiments evaluation of a passive knee-assisting exoskeleton for weight-climbing

Purpose This paper aims to investigate weight-climbing assistance strategy for the biomechanical design of passive knee-assisting exoskeleton (PKAExo) and evaluate a designed PKAExo which stores energy when the knee joint flexes and releases the energy to assist ascending when the knee joint extends. Design/methodology/approach The authors constructed theoretic modeling of human weight-climbing to analyze characteristics of knee angle and moment. They then conducted camera-based movement analysis, muscle strength and endurance tests and surface electromyography (sEMG) measures to verify the relationship of knee angle and moment with both stair height and load weight. Afterwards, the authors proposed an assistant strategy for passive knee assistance, then gave out designed PKAExo and conducted mechanical experiment to test the knee-assisting torque. Finally, the authors conducted comparison experiment based on measuring the sEMG signals of knee extensor to verify the assistance effect of the PKAExo for weight-climbing. Findings The knee extensor produces the maximum force during weight-climbing, and the muscle force provided by knee extensor has significant increasing rate along with the stair height. Thus, the assistance torque of PKAExo is designed to increase nonlinearly along with increasing knee angle. It stores energy when knee flexes and assists when knee extends. Both the mechanical experiment and comparison experiment have demonstrated that the PKAExo is able to provide nonlinear assistance torque for weight-climbing, thus decreasing the average maximum load of knee extensor by about 21 per cent, reducing muscle fatigue and enhancing wearer’s weight-climbing ability. Originality/value The authors construct theoretic maximum force model produced by knee extensor for weight-climbing in static situation and conduct a series of experiments to verify and revise the model, which is the fundamental reference for knee-assisting mechanism designed for weight-climbing. The authors have also provided and validated an assistant strategy and the mechanism based on the biomechanical analysis, which aims to translate wearer’s energy-providing mode form high load to mid-low load by storing energy when knee flexes and assisting when knee extends. The PKAExo decreases the maximum load of knee extensor, reduces muscle fatigue and helps people to easily climb with load.

Calculation of Metalwork Life with Allowance for Cyclic Degradation of Material in Operation

The article describes an alternative method of calculating durability and life of metal construction elements. Parameters of complete deformation diagram are used as a representative of the fatigue process. Such diagram is plotted when a small sample of material is stretched in a rigid load-applying unit. Determination of process kinetics from a mechanical experiment enhances possibilities for phenomenological description of constructional elements’ fatigue fracture. Proper usage of material cyclic degradation model in the stage of fatigue crack development is possible when one explicitly allows for anomalies of a constructional element’s surface layer properties. Within the scope of general concept of correlation between static and cyclic material properties a scheme for differentiating between a component’s surface layer and base metal properties is presented. Explicitly allowing for anomalies of a component’s surface layer properties makes it possible to calculate its durability and life within the unified model of material.