The ankle joint (AJ) is a crucial joint in daily life, responsible for providing stability, mobility, and support to the lower limbs during routine activities such as walking, jumping, and running. Ankle joint injuries can occur due to sudden twists or turns, leading to ligament sprains, strains, fractures, and dislocations that can cause pain, swelling, and limited mobility. When AJ trauma occurs, joint instability happens, causing mobility limitations or even a loss of joint mobility, and rehabilitation therapy is necessary. AJ rehabilitation is critical for those recovering from ankle injuries to regain strength, stability, and function. Common rehabilitation methods include rest, ice, compression, and elevation (RICE), physical therapy, ankle braces, and exercises to strengthen the surrounding muscles. Traditional rehabilitation therapies are limited and require constant presence from a therapist, but technological advancements offer new ways to fully recover from an injury. In recent decades there has been an upswing in research on robotics, specifically regarding rehabilitation. Robotic platforms (RbPs) offer several advantages for AJ rehabilitation assistance, including customized training programs, real-time feedback, improved performance monitoring, and increased patient engagement. These platforms use advanced technologies such as sensors, actuators, and virtual reality to help patients recover quicker and more efficiently. Furthermore, RbPs can provide a safe and controlled environment for patients who need to rebuild their strength and mobility. They can enable patients to focus on specific areas of weakness or instability and provide targeted training for faster recovery and reduced risk of re-injury. Unfortunately, high costs make it difficult to implement these systems in recuperative institutions, and the need for low-cost platforms is apparent. While different systems are currently being used, none of them fully satisfy patient needs or they lack technical problems. This paper addresses the conception, development, and implementation of rehabilitation platforms (RPs) that are adaptable to patients’ needs by presenting different design solutions (DSs) of ankle RPs, mathematical modeling, and simulations of a selected rehabilitation platform (RP) currently under development. In addition, some results from practical tests of the first prototype of this RP are presented. One patient voluntarily agreed to use this platform for more rehabilitation sessions on her AJ (right leg). To counteract some drawbacks of the first prototype, some improvements in the RP design have been proposed. The results on testing the improved prototype will be the subject of future work.

A major objective of tribological researches is characterisation of rolling friction, due to various cases encountered in classical engineering applications, like gear transmissions and cam mechanisms or more recent examples met in bioengineering and biomedical devices. A characteristic of these examples consists in reduced dimensions of the contact zones, theoretically zero, the relative motion occurring between the contact points being either sliding or rolling. A characteristic parameter for the rolling motion is the coefficient of rolling friction. The paper proposes a method for estimation of coefficient of rolling friction by studying the motion of a body of revolution on an inclined plane. Assuming the hypothesis that moment of rolling friction is proportional to the normal reaction force, the law of motion for the body on the inclined plane is found under the premise of pure rolling. It is reached the conclusion that there is an uniformly accelerated motion, and thus for a known plane slope, it is sufficient to find the time during which the body runs a certain distance, starting from motionless situation. To obtain accurate results assumes finding precisely the time of motion. The coefficient of rolling friction was estimated for several slopes of the inclined plane and it is concluded that with increased slope, the values of coefficient of rolling friction increase, fact that suggest that the proportionality between the rolling torque and normal load is valid only for domains of limited variations of normal load.

The paper presents a new solution of tripod joint. The kinematical analysis is obtained for the general case in analytical form. For the general case, the transmission ratio is variable. The solution found for relative displace-ments between the elements of tripod joint is found analytically and allows obtaining the relative trajectory of the centers of spheres in the symmetry planes of the grooves. The analytical results are validated using an analysis with numerical model. For the particular case of equidistant spider arms and grooves respectively, the transmission ratio becomes constant. The manufacturing of the transmission can be obtained using only lower pairs and thus substantially decreasing the contact stresses, proved by FEA method. Further more, the lack from the actual mechanism of cylindrical joints reduces the risk of self-locking phenomenon. DOI: http://dx.doi.org/10.5755/j01.mech.19.5.5539

The paper presents a method for experimental finding of coefficient of rolling friction appropriate for biomedical applications based on the theory of cycloidal pendulum. When a mobile circle rolls over a fixed straight line, the points from the circle describe trajectories called normal cycloids. To materialize this model, it is sufficient that a small region from boundary surfaces of a moving rigid body is spherical. Assuming pure rolling motion, the equation of motion of the cycloidal pendulum is obtained - an ordinary nonlinear differential equation. The experimental device is composed by two interconnected balls rolling over the material to be studied. The inertial characteristics of the pendulum can be adjusted via weights placed on a rod. A laser spot oscillates together to the pendulum and provides the amplitude of oscillations. After finding the experimental parameters necessary in differential equation of motion, it can be integrated using the Runge-Kutta of fourth order method. The equation was integrated for several materials and found values of rolling friction coefficients. Two main conclusions are drawn: the coefficient of rolling friction influenced significantly the amplitude of oscillation but the effect upon the period of oscillation is practically imperceptible. A methodology is proposed for finding the rolling friction coefficient and the pure rolling condition is verified.

The stress state from an eccentric ring made of an elastic material symmetrically loaded on the outer boundary by concentrated forces is deduced. The analytical results are obtained using the Airy stress function expressed in bipolar coordinates. The elastic potential corresponding to the same loading but for a compact disk is first written in bipolar coordinates, then expanded in Fourier series, and after that, an auxiliary potential of a convenient form is added to it in order to impose boundary conditions. Since the inner boundary is unloaded, boundary conditions may be applied directly to the total potential. A special focus is on the number of terms from Fourier expansion of the potential in bipolar coordinates corresponding to the compact disk as this number influences the sudden increase if the coefficients from the final form of the total potential. Theoretical results are validated both by using finite element software and experimentally through the photoelastic method, for which a device for sample loading was designed and constructed. Isochromatic fields were considered for the photoelastic method. Six loading cases for two different geometries of the ring were studied. For all the analysed cases, an excellent agreement between the analytical, numerical and experimental results was achieved. Finally, for all the situations considered, the stress concentration effect of the inner hole was analytically determined. It should be mentioned that as the eccentricity of the inner hole decreases, the integrals from the relations of the total elastic potential present a diminishing convergence in the vicinity of the inner boundary.