Background: This study aimed to investigate kinematic parameters of lower limb joints during gait on inclined SURFACES compared to level ground. Methods: In this cross-sectional study, 15 healthy individuals walked at their self-selected speed on level ground with a zero slope and on two inclined SURFACES. These SURFACES were constructed to mimic real environments with slopes of +8 (uphill) and -8 (downhill) along an eight-meter distance. The measured variables included the angles of the ankle, knee, and hip joints sagittal plane during different phases of gait, captured through a three-dimensional motion capture system. Results: Significant differences were observed in uphill walking compared to level-ground walking, including an increase in ankle, hip, and knee angles at initial contact, maximum ankle dorsiflexion and plantarflexion, maximum knee flexion in the stance phase, and maximum knee extension in the swing phase. There was also a reduction in the maximum extension of the hip joint (P<0.05). In downhill walking compared to level ground, significant differences were observed in the increase of ankle and knee angles at initial contact, maximum ankle dorsiflexion, maximum knee flexion in both stance and swing phases, and a decrease in the maximum angle of hip extension. However, no significant difference was observed in the hip joint angle at initial contact maximum ankle plantarflexion, maximum knee extension in swing phase between level and downhill SURFACES and at maximum knee flexion in swing phase between uphill and level SURFACES (P>0.05). Conclusion: Walking on inclined SURFACES influences the flexion and extension angles of lower limb joints during different phases of gait, necessitating increased joint movement. These alterations are more pronounced during uphill walking than downhill, especially at the initial contact point.

Purpose: Forward Walking (FW) and Backward Walking (BW) on different gradients of the treadmill is a common exercise for lower extremity rehabilitation. However, limited studies are found about the three-dimensional analysis of lower extremity and status of the knee joint during FW and BW on different gradients. Therefore, this study aimed to investigate the lower extremity joints kinematics during FW and BW on incline and decline SURFACES.Methods: The current research has a quasi-experimental design. Sixteen healthy males with the mean (SD) age of 22.4 (2.5) years, volunteered to participate in this study. The subjects’ FW and BW with their preferred speed on a treadmill at four gradients (-7.5%, 0%, +5% and+10%), were analyzed by using motion capture system. All data were analyzed using paired sample t test (P<0.05).Results: Significant differences were seen between FW and BW in most angular variables in sagittal plane. However, there were no significant differences between FW and BW in most parameters of knee angle in frontal plane.Conclusion: Based on the results, with increase in FW inclination and decrease in BW inclination, the knee varus angle in frontal plane reduces. Therefore, FW on the upslope SURFACES or BW on downslope SURFACES, probably is a suitable solution to reduce the loads exerted on medial compartment of the knee.

Since the one of the application of piano keys weir is use in irrigation and drainage network, and it is possible that with decrease of discharge, the water level during dehydration is faced with a drastic reduction. Therefore, by creating Parapet wall with the ability to change slope, can be allowed to weir, that any decrease in discharge, keep the water level at a certain level. In the present study, the important parameters affecting the discharge rate including of P/Wu, (weir height, P, to within one cycle width, Wu=Wi+Wo+2Ts) and SLOPED parapet wall were investigated. Then the equations of discharge coefficient with modifying the general equation weirs and dimensional analysis were obtained. To achieve these purposes, the parapet walls were built at three angles 3, 5.5 and 8 degrees in the direction of flow (positive) and the opposite (negative), on two piano key weirs, with ratios of P/Wu=1.33 (Model 1) and P/Wu=0.5 (model 2).The experiments have been carried out on a experimental flume with a width of 80cm, length 10m and a height of 60cm. The results showed that the model 1 with negative slope of 3 degrees can discharge more than the ogee weir (approximately 2.4 times). In addition, the derived relationship for the discharge coefficient (SLOPED parapet wall) had R2 equal to 0.978 and statistical indicators NRMSE and WQD equal to 0.0214 and 0.018, respectively.

The present study investigated the characteristics of hydraulic parameters of SLOPED Gabion Drops and Simple Drops. Therefore, 120 different experiments were performed on both types of SLOPED gabion drop and SLOPED simple drop with three angles and two heights. Results showed that by increasing the relative critical depth in both tested models, causes a reduction in relative energy dissipation rate but an increase in relative downstream depth. Comparing the results for SLOPED gabion drops and SLOPED simple drops showed that the use of gabion structures with three angles and two heights which, have been investigated, increases the average energy dissipation efficiency 561% and the average downstream relative depth 50. 1% compared to the simple drops. So, this results in a decrease in the erosion of the downstream bed of the structure and the length of the pool. The results showed that as the angle of incline increases, the average energy dissipation efficiency decreases and, the average downstream relative depth increases. The results showed that the change in the angle of the incline in SLOPED gabion drops had a relatively small effect, in comparison with the simple drops due to the physical properties and the complex hydraulic effects of the flow through the porous structure. Also, some relationships were presented to estimate the relative energy dissipation rate and the downstream relative depth rate in the SLOPED gabion drops by using 80% percent of laboratory data, and the rest 20% of the data were used to test the relationships with the evaluation criteria.

The rectangular broad crested weirs are widely used to measure the water discharge which is one of the most popular tools in the irrigation canals particularly, in developing countries.The present article is trying to demonstrate the results of an experimental work carried out on rectangular broad crested weir with SLOPED upstream face to investigate the effect of upstream slope on discharge efficiency. The upstream slope was varying from 90 to 23 degrees while incoming discharge was ranging from 14 to 75 lit/ sec. The experiments were conducted in a flume with a weir of fixed height under the normal downstream water depth .It is revealed that the slope of upstream face in rectangular broad crested weir would smoothen the flow profile having the critical depth on the weir crest adjacent and upstream of downstream edge of the weir . The results also lead to a novel achievement showing that the weir discharge efficiency is dependent on the slope of upstream face of the weir. As the slope of upstream face of the rectangular broad crested weir is decreasing from 90 to 23 the weir discharge efficiency is increasing and reaching to its maximum through a parabola function at slope angle of 25 degrees(i.e. 1:2.15). The investigation also showed that the depth of flow over the weir crest, the specific energy head of the approaching flow relative to chanel bed and the critical depth would be a pertinent similarity scales to asses the flow behavior over different SLOPED rectangular broad crested weirs between model and prototype. However, some broad investigation is recommended to endorse the achievements.

In this paper, we classify SURFACES at a constant distance from the edge of regression on a translation surface of Type 1 in the three dimensional simply isotropic space I13 satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental forms of the surface. We also give explicit forms of these SURFACES.