Mechanical: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=199
en-us2020 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 29 Mar 2020 04:03:10 GMTSun, 29 Mar 2020 04:03:10 GMTNew applications in the Mechanical categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgMechanical: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=199
Atwood Machine
https://www.maplesoft.com/applications/view.aspx?SID=154598&ref=Feed
The following is a detailed study of the motion of an unconventional Atwood Machine where one mass is constrained to move along a fixed vertical axis.
The differences with the regular Atwood Machine are :
1- the tension T on the string on either side of the pulley though it is the same, however it is not constant in the present case because of the obliquity of the 2d part of the string.
2- the unique and constant acceleration (a) in the simple machine is replaced in here with two different and variable accelerations whose ratio is however constant.
3- In the simple machine the constant acceleration makes plotting and animation of the system a straightforward procedure according to
s = (1/2)*at^2.However in the modified Atwood machine that we present in here the accelerations being variable there is no way to get the displacement as a direct function of time. This seems to make plotting & animation an impossible task. However we were able to devise a trick to overcome this difficulty.<img src="https://www.maplesoft.com/view.aspx?si=154598/Modified_Atwood_Machine.jpg" alt="Atwood Machine" style="max-width: 25%;" align="left"/>The following is a detailed study of the motion of an unconventional Atwood Machine where one mass is constrained to move along a fixed vertical axis.
The differences with the regular Atwood Machine are :
1- the tension T on the string on either side of the pulley though it is the same, however it is not constant in the present case because of the obliquity of the 2d part of the string.
2- the unique and constant acceleration (a) in the simple machine is replaced in here with two different and variable accelerations whose ratio is however constant.
3- In the simple machine the constant acceleration makes plotting and animation of the system a straightforward procedure according to
s = (1/2)*at^2.However in the modified Atwood machine that we present in here the accelerations being variable there is no way to get the displacement as a direct function of time. This seems to make plotting & animation an impossible task. However we were able to devise a trick to overcome this difficulty.https://www.maplesoft.com/applications/view.aspx?SID=154598&ref=FeedSat, 25 Jan 2020 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyOptimizing the Design of a Helical Spring
https://www.maplesoft.com/applications/view.aspx?SID=154000&ref=Feed
The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.
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Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.
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This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency, the maximum stress, and a loading condition.
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The design variables are the diameter of the wire, the outside diameter of the spring, and the number of coils.<img src="https://www.maplesoft.com/view.aspx?si=154000/helical_spring.png" alt="Optimizing the Design of a Helical Spring" style="max-width: 25%;" align="left"/>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.
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Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.
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This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency, the maximum stress, and a loading condition.
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The design variables are the diameter of the wire, the outside diameter of the spring, and the number of coils.https://www.maplesoft.com/applications/view.aspx?SID=154000&ref=FeedTue, 26 Nov 2019 05:00:00 ZSamir KhanSamir KhanPole simulation with tensions
https://www.maplesoft.com/applications/view.aspx?SID=154577&ref=Feed
Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154577/structure.png" alt="Pole simulation with tensions" style="max-width: 25%;" align="left"/>Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154577&ref=FeedMon, 14 Oct 2019 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloForces in a 4 Member Frame
https://www.maplesoft.com/applications/view.aspx?SID=154542&ref=Feed
This frame is subject to a load P at point G. This application will determine the forces at the supports and in members BE and CF.
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Since the frame is in equilibrium, the sum of horizontal forces, sum of vertical forces, and sum of momentum about a point is zero. This allows us to identify the unknown forces in a system.<img src="https://www.maplesoft.com/view.aspx?si=154542/frame.png" alt="Forces in a 4 Member Frame" style="max-width: 25%;" align="left"/>This frame is subject to a load P at point G. This application will determine the forces at the supports and in members BE and CF.
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Since the frame is in equilibrium, the sum of horizontal forces, sum of vertical forces, and sum of momentum about a point is zero. This allows us to identify the unknown forces in a system.https://www.maplesoft.com/applications/view.aspx?SID=154542&ref=FeedMon, 08 Jul 2019 04:00:00 ZSamir KhanSamir KhanKinematic Analysis of a Quick Return Device
https://www.maplesoft.com/applications/view.aspx?SID=154541&ref=Feed
This is a quick return device.
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This application will:
<UL>
<LI>determine the range of motion of this device
<li>and its behavior if the crank driven at (i) a constant angular velocity, and (ii) a constant angular acceleration
</UL>
The latter involves numerically solving differential equations. These are symbolically derived by differentiating the geometric relationships with respect to time. The resulting equations contain the first and second derivative of the crank angle with respect to time; these will be set to constant values to reveal the behavior of the system.<img src="https://www.maplesoft.com/view.aspx?si=154541/kinematic.png" alt="Kinematic Analysis of a Quick Return Device" style="max-width: 25%;" align="left"/>This is a quick return device.
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This application will:
<UL>
<LI>determine the range of motion of this device
<li>and its behavior if the crank driven at (i) a constant angular velocity, and (ii) a constant angular acceleration
</UL>
The latter involves numerically solving differential equations. These are symbolically derived by differentiating the geometric relationships with respect to time. The resulting equations contain the first and second derivative of the crank angle with respect to time; these will be set to constant values to reveal the behavior of the system.https://www.maplesoft.com/applications/view.aspx?SID=154541&ref=FeedMon, 08 Jul 2019 04:00:00 ZSamir KhanSamir KhanPositions of Two Objects Suspended and Connected by Ropes
https://www.maplesoft.com/applications/view.aspx?SID=154535&ref=Feed
Two objects are connected and suspended by a system of ropes, as illustrated in the diagram.
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This application finds the position of the objects and the tension in the ropes with a horizontal and vertical force balance.<img src="https://www.maplesoft.com/view.aspx?si=154535/thumb.png" alt="Positions of Two Objects Suspended and Connected by Ropes" style="max-width: 25%;" align="left"/>Two objects are connected and suspended by a system of ropes, as illustrated in the diagram.
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This application finds the position of the objects and the tension in the ropes with a horizontal and vertical force balance.https://www.maplesoft.com/applications/view.aspx?SID=154535&ref=FeedWed, 05 Jun 2019 04:00:00 ZSamir KhanSamir KhanSystem of Equations 2x2 and 3x3
https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=Feed
This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154520/sis_eq_dpd.png" alt="System of Equations 2x2 and 3x3" style="max-width: 25%;" align="left"/>This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=FeedTue, 19 Mar 2019 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloEquilibrium Positions of Two Objects Connected by Ropes
https://www.maplesoft.com/applications/view.aspx?SID=154495&ref=Feed
Two objects are connected and suspended by a system of ropes, as illustrated below.
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These parameters are known
<UL>
<LI>the object weights, w1 and w2
<LI>the length of the ropes L1, L2, and L3
<LI>the anchor points (x1, y1) and (x4, y4)
</UL>
The objects positions and the rope tensions are calculated from a numeric solution of the equations that describe
<UL>
<LI>horizontal and vertical force balances
<LI>and the constraints imposed by the lengths of the ropes
</UL><img src="https://www.maplesoft.com/view.aspx?si=154495/equilibrium.png" alt="Equilibrium Positions of Two Objects Connected by Ropes" style="max-width: 25%;" align="left"/>Two objects are connected and suspended by a system of ropes, as illustrated below.
<BR><BR>
These parameters are known
<UL>
<LI>the object weights, w1 and w2
<LI>the length of the ropes L1, L2, and L3
<LI>the anchor points (x1, y1) and (x4, y4)
</UL>
The objects positions and the rope tensions are calculated from a numeric solution of the equations that describe
<UL>
<LI>horizontal and vertical force balances
<LI>and the constraints imposed by the lengths of the ropes
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154495&ref=FeedThu, 04 Oct 2018 04:00:00 ZSamir KhanSamir KhanPlot of curvature and radius of curvature
https://www.maplesoft.com/applications/view.aspx?SID=154486&ref=Feed
This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.<img src="https://www.maplesoft.com/view.aspx?si=154486/radcurv.png" alt="Plot of curvature and radius of curvature" style="max-width: 25%;" align="left"/>This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.https://www.maplesoft.com/applications/view.aspx?SID=154486&ref=FeedMon, 03 Sep 2018 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloKinematics Curvilinear
https://www.maplesoft.com/applications/view.aspx?SID=154269&ref=Feed
With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154269/kc.png" alt="Kinematics Curvilinear" style="max-width: 25%;" align="left"/>With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154269&ref=FeedTue, 14 Nov 2017 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of equation impulse-momentum
https://www.maplesoft.com/applications/view.aspx?SID=154347&ref=Feed
In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.<img src="https://www.maplesoft.com/view.aspx?si=154347/mivis.png" alt="Plot of equation impulse-momentum" style="max-width: 25%;" align="left"/>In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.https://www.maplesoft.com/applications/view.aspx?SID=154347&ref=FeedTue, 17 Oct 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMoment of a force using vectors
https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=Feed
The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154345/moment of force.PNG" alt="Moment of a force using vectors" style="max-width: 25%;" align="left"/>The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=FeedTue, 26 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloVector space with projections and forces
https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=Feed
With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154294/vectors.PNG" alt="Vector space with projections and forces" style="max-width: 25%;" align="left"/>With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=FeedMon, 11 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDisplacement and distance traveled with vectors
https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=Feed
In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154293/desplvp.png" alt="Displacement and distance traveled with vectors" style="max-width: 25%;" align="left"/>In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=FeedMon, 28 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of Position Vector
https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=Feed
This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154290/bnrvp.png" alt="Plot of Position Vector" style="max-width: 25%;" align="left"/>This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=FeedThu, 10 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMomentum with two variable force
https://www.maplesoft.com/applications/view.aspx?SID=154273&ref=Feed
This app shows the calculation of the final velocity of a body after it made contact with a variable force taking as reference the initial velocity, mass and the graph of the variation of F as a function of time. Made with native maple syntax (use of promt) and embedded components.
In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154273/cmimp.png" alt="Momentum with two variable force" style="max-width: 25%;" align="left"/>This app shows the calculation of the final velocity of a body after it made contact with a variable force taking as reference the initial velocity, mass and the graph of the variation of F as a function of time. Made with native maple syntax (use of promt) and embedded components.
In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154273&ref=FeedTue, 04 Jul 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloKinematics using syntax
https://www.maplesoft.com/applications/view.aspx?SID=154271&ref=Feed
In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154271/kinematicssint.png" alt="Kinematics using syntax" style="max-width: 25%;" align="left"/>In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154271&ref=FeedWed, 14 Jun 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloUniversal method of kinematic analysis of spatial and planar link mechanisms
https://www.maplesoft.com/applications/view.aspx?SID=154228&ref=Feed
The application of idea Draghilev method of solving systems of nonlinear equations for the kinematic analysis of link mechanisms with any number degrees of freedom.<img src="https://www.maplesoft.com/view.aspx?si=154228/fig_2.jpg" alt="Universal method of kinematic analysis of spatial and planar link mechanisms" style="max-width: 25%;" align="left"/>The application of idea Draghilev method of solving systems of nonlinear equations for the kinematic analysis of link mechanisms with any number degrees of freedom.https://www.maplesoft.com/applications/view.aspx?SID=154228&ref=FeedWed, 08 Mar 2017 05:00:00 ZAlexey IvanovAlexey IvanovStatically Indeterminate Structure
https://www.maplesoft.com/applications/view.aspx?SID=153940&ref=Feed
The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.<img src="https://www.maplesoft.com/view.aspx?si=153940/391e24e981ea8d11454375def604a185.gif" alt="Statically Indeterminate Structure" style="max-width: 25%;" align="left"/>The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.https://www.maplesoft.com/applications/view.aspx?SID=153940&ref=FeedWed, 09 Mar 2016 05:00:00 ZDr. Aleksey ShirkoDr. Aleksey ShirkoFuel Pod Design Optimization
https://www.maplesoft.com/applications/view.aspx?SID=153998&ref=Feed
A manufacturer has designed a fuel pod in NX. The fuel pod has a hemispherical and conical end, and a cylindrical midsection.
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To minimize material costs, the manufacturer wants to minimize the surface area of the fuel pod while maintaining the existing volume.
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This application:
<UL>
<LI>pulls the current dimensions of the fuel pod (radius of the hemispherical end, length of the cylindrical midsection, and height of the conical end) from the NX CAD model,
<LI>calculates the current volume of the fuel pod,
<LI>optimizes the dimensions to minimize the surface area while maintaining the existing volume,
<LI>and pushes the optimized dimensions back into the NX CAD model.
</UL><img src="https://www.maplesoft.com/view.aspx?si=153998/fuel_pod.png" alt="Fuel Pod Design Optimization" style="max-width: 25%;" align="left"/>A manufacturer has designed a fuel pod in NX. The fuel pod has a hemispherical and conical end, and a cylindrical midsection.
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To minimize material costs, the manufacturer wants to minimize the surface area of the fuel pod while maintaining the existing volume.
<BR><BR>
This application:
<UL>
<LI>pulls the current dimensions of the fuel pod (radius of the hemispherical end, length of the cylindrical midsection, and height of the conical end) from the NX CAD model,
<LI>calculates the current volume of the fuel pod,
<LI>optimizes the dimensions to minimize the surface area while maintaining the existing volume,
<LI>and pushes the optimized dimensions back into the NX CAD model.
</UL>https://www.maplesoft.com/applications/view.aspx?SID=153998&ref=FeedWed, 02 Mar 2016 05:00:00 ZSamir KhanSamir Khan