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ECM3163 Mechanical Engineering Design Studies

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ECM3163 Mechanical Engineering Design Studies

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Course Code: ECM3163
University: University Of Exeter

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Country: United Kingdom

Questions:
1. Summarise the constraints, objectives, etc. of material selection in the main report, and include more details of the Material index, and screening processes.
2. Outline the literature and justification relating to an innovative material or manufacturing process in the main report, with more in-depth analysis

Answer:
Introduction
Prior to the development of efficient tools that aid patients with lost lower limbs, people only had the option of wheelchairs, walkers, crutches, and wooden pen legs in the event that they have lower half body amputation or paralysis. Nonetheless, in today’s contemporary world, there are numerous options available for patients with lost lower limbs including motorized limb prosthetic giving these victims a good chance of restoring full mobility regardless of their circumstance.Problem Statement The lower limb as a whole systems contributes significantly to how the body functions. The legs provide support and balance whilst we walk or stand while the knees create a connection between the lower and the upper sections of the legs as well as supporting bending for ease of walking.Most of the prosthetic limbs available in the market based on the microcontroller active or semi active technology are too highly priced for the average person to be able to afford them while not considering the doubt of the input sensory data. This thereby means that only a select few can afford them though they are affected by input uncertainty which results in the decline of their effectiveness (Biddiss, Beaton, and Chau, 2007, p.351). Consequently, the purpose of this report is to expound on the design of the simple and low cost Lower Half Body Prosthesis that comes with modular sensors, aimed at the developing world. The mechanical parts of the Lower Half Body Prosthesis are uncomplicated to streamline maintenance and enable sturdiness.
Objectives
The medical device (Lower Half Body Prosthesis) is designed for people with either amputated lower limbs leg or are paralyzed from the waist down such that they can used the designed device. This trans-femoral medical Lower Half Body Prosthesis supplies the dynamic energy at the joint of the waist rather than using up the partial energy of the patient. Such prosthetic devices allow for the improved effectiveness and limited energy utilization when walking, jogging, running or even standing. A majority of the present smart limbs prosthetics depend on sensors implanted in them. Nevertheless, the Lower Half Body Prosthesis that has been proposed obtains data from the contra-lateral device.
Design Solution
The novelty of the design and mechanics of the Lower Half Body Prosthesis with its distinctive controller offers a likely and foreseeable future in the smart prosthetic industry. The theory behind the development of the Lower Half Body Prosthesis is to provide the user the assistance of walking a full gait cycle with little to no difficulty. This report combines the design of the mechanical structure of the prosthesis with the smart control computerized system that permits the development of a dynamic prosthetic medical device for easy mobility (Stepien, Cavenett, Taylor, and Crotty, 2007, p.897.)
Introduction
Prior to the development of efficient tools that aid patients with lost lower limbs, people only had the option of wheelchairs, walkers, crutches, and wooden pen legs in the event that they have lower half body amputation or paralysis. Nonetheless, in today’s contemporary world, there are numerous options available for patients with lost lower limbs including motorized limb prosthetic giving these victims a good chance of restoring full mobility regardless of their circumstance.
Problem Statement
The lower limb as a whole systems contributes significantly to how the body functions. The legs provide support and balance whilst we walk or stand while the knees create a connection between the lower and the upper sections of the legs as well as supporting bending for ease of walking.
Most of the prosthetic limbs available in the market based on the microcontroller active or semi active technology are too highly priced for the average person to be able to afford them while not considering the doubt of the input sensory data. This thereby means that only a select few can afford them though they are affected by input uncertainty which results in the decline of their effectiveness (Biddiss, Beaton, and Chau, 2007, p.351). Consequently, the purpose of this report is to expound on the design of the simple and low cost Lower Half Body Prosthesis that comes with modular sensors, aimed at the developing world. The mechanical parts of the Lower Half Body Prosthesis are uncomplicated to streamline maintenance and enable sturdiness.
Objectives
The medical device (Lower Half Body Prosthesis) is designed for people with either amputated lower limbs leg or are paralyzed from the waist down such that they can used the designed device. This trans-femoral medical Lower Half Body Prosthesis supplies the dynamic energy at the joint of the waist rather than using up the partial energy of the patient. Such prosthetic devices allow for the improved effectiveness and limited energy utilization when walking, jogging, running or even standing. A majority of the present smart limbs prosthetics depend on sensors implanted in them. Nevertheless, the Lower Half Body Prosthesis that has been proposed obtains data from the contra-lateral device.
Design Solution
The novelty of the design and mechanics of the Lower Half Body Prosthesis with its distinctive controller offers a likely and foreseeable future in the smart prosthetic industry. The theory behind the development of the Lower Half Body Prosthesis is to provide the user the assistance of walking a full gait cycle with little to no difficulty. This report combines the design of the mechanical structure of the prosthesis with the smart control computerized system that permits the development of a dynamic prosthetic medical device for easy mobility (Stepien, Cavenett, Taylor, and Crotty, 2007, p.897.)
Literature Review
(Legro, et al., 2008, p. 934) argues that the demand for medical prosthetics is always on the rise occasioned by the high number of ex-veterans who are casualties of war, accidents from different activities  and the many recently emerging diseases that could lead to any form of paralysis. The high numbers of UXOs (Unexploded Ordinance) tools endanger the wellbeing of millions of inhabitants of developing regions including the Middle East, and parts of Africa. Very many people are rendered disabled or in worse case scenarios dead due to these devices. Focusing solely on war torn countries, it is evident that there is huge demand for medical prosthetics. Further (Biddiss, Beaton, and Chau, 2007, p.346) paints the picture that armed conflict has on children. The author argues that due to the fact that the bones of children take a shorter time to grow than the adjacent tissue, the affected child may need recurred amputations and new medical prosthetics every half year. Sadly though, the high price of these artificial limbs keeps such children from accessing them.
According to (Shurr, Michael, and Cook, 2002, p.67) the type of material used in the development of the Lower Half Body Prosthesis is extremely important. This is because altering the material changes the physical properties of the entire device including the overall weight and sturdiness. Lim adds that the outline of FEA (Finite Element Analysis) and expansion part of the Lower Half Body Prosthesis is included. Nonetheless, Lim adds that the results of material properties on the Lower Half Body Prosthesis system will not be included.Legro and the other authors propose a connected wholly dynamic Lower Half Body Prosthesis ran by an electric motor and a gear lessening mechanism. The two have tried decreasing the patient’s power cost by supplying wholly powered trans-femoral limbs (Legro, et al., 2008, p.937). A methodology on the determination of the best size of the motor for a powered medical prosthetic was also proposed.
(Laurentis and Mavroidis, 2002, p.94) proposes that the Lower Half Body Prosthesis ought to meet the demands of a range of different demographics. Therefore a modular construction and the capacity to adapt to a wide range of measurements are important to attain adaptability at such levels. According to Laurentis and Mavroidis, the research of anthropometry centers its study on the human anatomy, where personal body height is determined in order to calculate bone length and thus the suitable size of Lower Half Body Prosthesis for every individual.
Mechanical Design
Design Features
The Lower Half Body Prosthesis was created in three mechanical design stages. The key target of the Lower Half Body Prosthesis was to develop a medical prosthetic device that is minute and non-heavy enough to be adapted by a wide array of people. Through the use of anthropometry and the analysis of the human mechanism, the Lower Half Body Prosthesis was developed with a broad demographic array in mind. Furthermore, the prosthetic limb was designed with the use of aluminum grade 6061 which is very light and nimble. Aluminum was preferred because it is both cheap and readily available, though there are lighter materials albeit very expensive (Herr, 2009, p.21). All the mechanical elements were made of aluminum except for the bought and already made components. The team also crafted the design to include the femoral stump and tibial extension. The key part of the Lower Half Body Prosthesis is the tibial section that supports the biggest loads and pressures and the waist attachment that guarantees security, safety, and shape of the designed device. The Lower Half Body Prosthesis is developed with great uneven cyclic impacts in mind, as well as the loads and pressures on the tibial nd waist components that make it effective.
In addition, the Lower Half Body Prosthesis is firm for the resistance of hard and coarse paths that the patient may find themselves in the lower limb joints are all simple parts of bearings of high-accuracy in double parallel arrangement, giving added torsion steadiness. The ball and hinge joints that facilitates adjusting of the limbs and different segments of the designs using  an alloy of chromium, nickel, and stainless steel. The Lower Half Body Prosthesis is designed with a 70kg person in mind (Herr, 2009, p.21).
The tibial section is designed in a semicircular shape which facilitates the resistance of compression in the coronal surface. This is also the case of the femoral segments of the design. The waist area makes allowances for adjustments for fitting, fixing, and maintetance. Moreover, the mechanics permit enhanced resistance to stress for the entire device. The tibial part is linked to the torque arm of the femoral section for both limbs with an alloy hinge joint of the knee, which gives the required dynamic torque to the joint mechanism of the Lower Half Body Prosthesis. The ball screw is the key system in the device, which supplies motion and support to the weight. The ball screw is enclosed in the motor chamber, where the servomotor is as well connected. The figure below illustrates the Lower Half Body Prosthesis.  Figure 1:Lower Half Body Prosthesis view:
The device is compact and light aiding in easy mobility of the user. 
The figure below shows an intricate view of the Lower Half Body Prosthesis structure. The prosthetic kneehas a total of 18 different and distinct screws, 12 bearings, and 13 separate components. 
Mechanical System
The artificial prosthetic limbs have to utilize a high speed motors whose role is to produce the amount of torque that is required to sufficiently derive the prosthetic limb. This is however limited by the operating peak speed which is specified for the system according to the design specification. The operating peak speed required is in the determination of the best speed of the prosthesis as well as its highest torque (Sup, Bohara, and Goldfarb, 2008, p.265). The limbs require that a gear reduction mechanism is connected to the design using a ball screw type of attachment which allows the final gear, such that the output of the final gear makes the limb move at a slower rotational velocity (ω). This translates to higher levels of torque emitted from the prosthetic limb, so that it would be beneficial for carrying out heavy work.  
A servomotor is also placed in the prosthesis in a parallel orientation to the ball screw, for the purposes of mobilizing the nut of the prosthesis using a belt drive. The nut of the prosthesis will be implanted in a pair of bearings so that the nut and the electro-motor are in a fixed position since they do not require relative motion against each other. The nut and electromotor will for this reason continue to rotate in their fixed place as a result of the bearings. The translational motion that is produced by the prosthesis limb is guaranteed by the ball-screw rotation and its motion relationship with the system of the belt drive (Legro, et al, 2008, p. 936).
The following diagram of the prosthesis limb indicates the hinge joint  system for the prosthesis which utilize the pulley mechanisms. The design is done in an adjustable manner such that the limbs can be tailor made to suit the frame of the users. The length of the arm is fixed between the joint of the limb and the ball-screw’s upper end. This leaves out an angle of named α that occurs between the axis of the arm and the central axis of the ball screw. This angle allows for the computation of the angular velocity and angular acceleration using the second order differential of time. The angular velocity (ω) is the rpm of the limb, classified as the rotational velocity of the limb  and the rotational velocity of the motor of the limb. 
The design of the screw is determined by the screw’s lead l which is computed through the multiplication of the pitch of the screw and the starts number of the screw. Taking the lead for this ball screw was taken to be 0.001m.  The linear velocity of the screw relates with the angular velocity of the limb following the relationship described below.  
Where  is the angular velocity of the limb
V is the linear velocity of the ball-screw axis
r is the length of the arm between the joint and the ball-screw end
The linear velocity v, can also be computed  as a consequence of the rotation of the nut of the ball screw following the following formula. 
Where is the angular velocity of the ball-screw and depends on the velocity of the motor and the gear reduction 
Combining the three equations, 
Taking the angular velocity of the limbs of the prosthesis to be 3.1416rad/s, the above equation can be used to compute the maximum angular velocity of the motor. The angular velocity of the motor () for the  was found to be 604. 84 rad/s. 
Where F is the applied force of the ball-screw
The torque that is needed in the ball-screw nut to provide the push and pull for the prosthesis 
Where is the applied torque from the ball screw of the nut
N is the efficiency.
This equation assumes that the friction experienced in the limbs of the prosthesis is of a negligible level. The torque produced in the screw  can also be related to the torque applied from the electromotor Tm following the equation below. 
Combining the three equations that relate the torque, can be used to derive an expression relating the torque of the limb to the torque that is applied by the electro-motor torque. 
Where  is the overall efficiency
The  is derived as a function of all the moving parts which has been computed to be 41.34%. Using the operating range of the limbs in this equation will aid to find the maximum output of the torque to be 23.44Nm. This value of maximum torque is applied at the midpoint between the mid-stance into the toe-off while the maximum torque of the limb is important in the selection of the right electro-motor (Kang, Pendegrass, Marks, and Blunn, 2010, p. 1136)
Degrees of Freedom (DOF)
The methodology used in the calculation of the degrees of freedom for the Lower Half Body Prosthesis is the Gruebler’s Mobility Equation. This equation is modified using the Kutzbach modification as the degrees of freedom were established using planar considerations. The number of DOFs can be computed using the equation below. 
Where M is the DOFs for the entire system
N is the number of segments with fixed links
F1 is the number of joints with one DOF
F2 is the number of joints with 2 DOFs
The designed system was set to have a total of 5 DOFs and a main joint with 1DOF which is different from the actual limb joint which has 6-DOF. To guarantee the durability of the design and that it remains a low cost design, the design of the limbs was improvised to have a hinge mechanism that is simpler with only 1 DOF. The improvised design also contains different parts that resemble  the anatomy of the human limb, which is composed of the moment arm, the joint and the upper part of the tibia (Sup, Bohara, and Goldfarb, 2008, p. 263).This design principle was therefore the best for the design of  a Lower Half Body Prosthesis device.
Dynamics
The dynamics of the prosthesis are derived through second-order ODEs (Ordinary Differential Equations) which describes and governs motion in the human limbs. Lower Half Body Prosthesis require to be modelled as a manipulator that utilizes fixed links in order to bring about motion. Equations of motion can therefore be differentiated using either the Lagrangian ODE and  Newton-Euler expressions which yield similar equations of motion.
The Newton-Euler expression is derived from the analysis of forces and moments acting between different parts of the prosthesis derived from Newton’s second law of motion. The equations that result from the expression include the equations that couple moments and forces through mathematical manipulation. These mathematical procedures are used for purposes of elimination of the extra terms that are not required in the computation of the dynamic components of the prosthesis. On the other hand, the Lagrangian expression is more straightforward as it employs the approach of considering energy equations in order to identify the dynamics of the prosthesis. This automatically considers the forces that do not do any work in the prosthesis (Miller, Deathe, and Speechley, 2011, p.1437). At the end of the day, the Lagrangian expression fails to consider the internal forces which are ignored. This makes this methodology even simpler than the use of Newton-Euler expression. This explains why the Lagrangian formulation was employed in this design project as they are able to propagate the equation of motion and thus unravel the inverse dynamics of the prosthesis required for the design of the permissible levels of torque for the actuators of the system.
Deriving the Dynamic Model using the Lagrangian Formulation
The prosthesis system utilizes an inverse dynamic model where the input parameters follow the trajectories that are desired for the specific position, velocity, and acceleration for the individual points. Guided by the knowledge of these parameters, the forces and the torques required at different points of the artificial limb are computed and utilized as the output parameters of the dynamic model of the prosthesis. The figure below illustrates the model of a human lower limb which is illustrated using the sinusoidal motion that occurs at the pelvis during motion following the movement of the waist and limbs while walking 
The distances between the center of mass for both the links namely the shank and the thigh, as well as the upper joint distance between the knee joint and the hip are denoted using r1 and r2 respectively. Further, the length of the tibia and the femur are denoted by L2 and L1 respectively. The tibia and femur’s angular positions are denoted using θ1 and θ2 is taken with respect to with the y-axis. The trunk can thus be taken as a vertical , such that the angle at the hip is equivalent to θ1 and the angle of the knee is equivalent to the angular position of the hank and the knee. Thus;
Discussion
Assumptions
The following are assumptions that were made to so that the Lagrangian Formulation could be effectively utilized in the dynamic modelling of the prosthetic limb.

The center of rotation at the joint is a fixed position
The center of mass is also a fixed position for each segment
The individual segments of the prosthesis are rigid bodies
The mass of the trunk of the prosthetic limb is negligible (Miller, Deathe, and Speechley, 2001, p.1436).

The dimensions of the center of mass distances and the length parameters have all been derived using the Anthropometric data for the lower body. 
The above is a free body diagram of the model such that the torques produced at the hip and the knee as the ball and hinge joints of the limb caused by the applied forces that continue to be felt on the tendons and  the ligaments of the limb. The angles that occur in this situation are denoted using θ1 and θ2 respectively while F1 and F2 denote both the vertical and horizontal components of force that emerge as a reaction to the ground force that is applied on the prosthesis at the center of pressure position. This position represents that planar position of the GRF. The forces acting on the femur caused by the socket are also represented in the free body diagram as Fox and Foy respectively.
Modeling of the Inclination Angle
The gait cycle also presents other characteristics of simple harmonic motion through the sagittal motion of the limbs. The figure below illustrates how the inclination model for this design project was modelled on the basis of the links within the limb, namely the shank and the thigh. 
This figure also models the motion of the knee and the hip joint in a simple  harmonic motion that is reiterative. The individual segments of the lower limb can thus be modelled as  the actuator controller input parameters in order to describe the angles of the joints on the lower limbs (Legro, et al., 2008, p.935).
The angle between the joints of the leg , waist and the individual segments making it up based on the reference given alongside. 
The full extension of the joints translate to no flexion degrees. This implies that when the angle at the thigh is greater than that at the leg ( the knee becomes flexed while the reverse caused the knee to remain extended.
Conclusion
The major objective of this design project was to guarantee that a Lower Half Body Prosthesis with the ability to reduce the amount of energy that amputees use during ambulation is successfully designed. This will be facilitated by the ability of the prosthesis to power the joint and thus allowing the amputees to use up less energy during ambulation. The other main objective was to offer a more cost effective solution for the amputees as most of the solutions in the market are expensive.
The design seeks to simplify the complex lower half body which is a section of the body with six degrees of freedom into a joint that utilizes a simple hinge which has one degree of freedom. The design will have a simple mechanical system to guarantee good accuracy in its control. This will be facilitated by installing a motor inside the prosthetic joint to drive the mechanism while the actuator of the design will need to be reinforced using a ball-screw methodology. The ball screw will offer a solution of gearing reduction which increases the amount of torque that the motor is expected to contribute. In so doing, the design project will overcome the challenge of the generation of inadequate torque which forces the amputees to apply more force during the stance phase (Miller, Deathe, and Speechley, 2001, p.1439).
The design was made with the aim of replicating the manner in which the human lower limbs function during ambulation. As such, the simulation of the movement was done using solid works software that can mimic how the femur is displaced within the limb during different activities and at different speeds aswell as the movement of the hips and the waist. The simulation of the hip joint was done on a solid works software which sought to model the pelvic displacements during motion. The reaction force from the ground was simulated with the aid of the software, so that the modelling conditions can imitate the motion of the entire lower limb on the ground during motion, thus conducting promoting the experimental analysis of the design (Herr, 2009, p.21).
Recommendations
As more studies continue to be conducted in the future to improve the design of the Lower Half Body Prosthesis, the following insights could be helpful to guarantee the success of the next project. The recommendations suggest that low level tasks be undertaken for purposes of improving and enlarging the design scope presented in this study. The other recommendation is that the development of new Lower Half Body Prosthesis designs are to be proposed  through high level tasks  with regard to the experiences gained during the design of this project.  
Bibliography
Biddiss, E., Beaton, D. and Chau, T., 2007. Consumer design priorities for upper limb prosthetics. Disability and Rehabilitation: Assistive Technology, 2(6), pp.346-357.
Herr, H., 2009. Exoskeletons and orthoses: classification, design challenges and future directions. Journal of neuro-engineering and rehabilitation, 6(1), p.21.
Kang, N.V., Pendegrass, C., Marks, L. and Blunn, G., 2010. Osseocutaneous integration of an intraosseous transcutaneous amputation prosthesis implant used for reconstruction of a transhumeral amputee: case report. The Journal of hand surgery, 35(7), pp.1130-1134.
Laurentis, K.J.D. and Mavroidis, C., 2002. Mechanical design of a shape memory alloy actuated prosthetic hand. Technology and Health Care, 10(2), pp.91-106.
Legro, M.W., Reiber, G.D., Smith, D.G., Del Aguila, M., Larsen, J. and Boone, D., 1998. Prosthesis evaluation questionnaire for persons with lower limb amputations: assessing prosthesis-related quality of life. Archives of physical medicine and rehabilitation, 79(8), pp.931-938.
Miller, W.C., Deathe, A.B. and Speechley, M., 2001. Lower extremity prosthetic mobility: a comparison of 3 self-report scales. Archives of physical medicine and rehabilitation, 82(10), pp.1432-1440.
Powers, C.M., Torburn, L., Perry, J. and Ayyappa, E., 1994. Influence of prosthetic foot design on sound limb loading in adults with unilateral below-knee amputations. Archives of physical medicine and rehabilitation, 75(7), pp.825-829.
Shurr, D.G., Michael, J.W. and Cook, T.M., 2002. Prosthetics and orthotics. Upper Saddle River, NJ: Prentice Hall.
Stepien, J.M., Cavenett, S., Taylor, L. and Crotty, M., 2007. Activity levels among lower-limb amputees: self-report versus step activity monitor. Archives of physical medicine and rehabilitation, 88(7), pp.896-900.
Sup, F., Bohara, A. and Goldfarb, M., 2008. Design and control of a powered transfemoral prosthesis. The International journal of robotics research, 27(2), pp.263-273.

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