Design and Mechanics of Lower Half Body Prosthesis

This report details the design and fabrication of a Lower Half Body Prosthesis based on the design of a simple and low cost lower half body prosthesis that will guarantee the user the assistance of walking a full gait cycle with little to no difficulty. The design will utilize modular sensors and distinctive controllers that follow recent developments in innovation to ensure the new design remains simple to streamline maintenance and enable sturdiness.

Design and Mechanics of Lower Half Body Prosthesis
Name
Institution

Design of a Lower Half Body Prosthesis 2
Executive Summary
This report details the design and fabrication of a Lower Half Body Prosthesis based on the
design of a simple and low cost lower half body prosthesis that will guarantee the user the
assistance of walking a full gait cycle with little to no difficulty. The design will utilize modular
sensors and distinctive controllers that follow recent developments in innovation to ensure the
new design remains simple to streamline maintenance and enable sturdiness.The design was
achieved through combining the design of the mechanical structure of the prosthesis with the
smart control computerized system, allowing the development of a dynamic prosthetic medical
device for easy mobility. The design employs engineering principles from literature including the
Lagrangian ODE expression which uses the approach of considering energy equations in order to
identify the dynamics of the prosthesis. The report also explores the requirements and the
specifications of the prosthesis. The design will have simple mechanics in its design including
distinctive controllers positively contribute to the 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.

Design of a Lower Half Body Prosthesis 3
Table of Contents
Table of Figures...........................................................................................................................................4
Introduction.................................................................................................................................................5
Problem Statement.................................................................................................................................5
Objectives................................................................................................................................................6
Design Solution........................................................................................................................................6
Literature Review........................................................................................................................................7
Mechanical Design.......................................................................................................................................8
Design Features.......................................................................................................................................8
Mechanical System................................................................................................................................13
Degrees of Freedom (DOF)....................................................................................................................17
Dynamics...............................................................................................................................................18
Deriving the Dynamic Model using the Lagrangian Formulation.......................................................19
Discussion..................................................................................................................................................21
Assumptions..........................................................................................................................................21
Modeling of the Inclination Angle.........................................................................................................22
Conclusion.................................................................................................................................................24
Recommendations.....................................................................................................................................25
Bibliography...............................................................................................................................................27
Appendices................................................................................................................................................29
Decision Matrices..................................................................................................................................29
List of Suppliers.....................................................................................................................................29
Calculations...........................................................................................................................................29
Numerical Analysis – Software Based....................................................................................................29
Gantt chart............................................................................................................................................29
Part and Assembly Drawings.................................................................................................................29

Design of a Lower Half Body Prosthesis 4
Table of Figures
Figure 1:Lower Half Body Prosthesis view:...............................................................................................10
Figure 2 Prosthetic limbs and how it will operate.....................................................................................12
Figure 3 Front view of prosthesis to show the different components like screws, bearings, and parts....13
Figure 4 Assembly of prosthesis................................................................................................................14
Figure 5 The hinge joint mechanics of the limbs......................................................................................16
Figure 6 A simplified model of the lower limb of a human........................................................................21
Figure 7 The free body diagram of the human lower limb........................................................................22
Figure 8 Motion of the legs while taking a stride.......................................................................................23
Figure 9 Inclination of the foot, thigh and shank angles............................................................................24
Figure 10Correlation between joint angles and inclination angles of different segments.........................25

Design of a Lower Half Body Prosthesis 5
Design of Artificial Limbs
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.

Design of a Lower Half Body Prosthesis 6
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.)

Design of a Lower Half Body Prosthesis 7
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

Design of a Lower Half Body Prosthesis 8
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

Design of a Lower Half Body Prosthesis 9
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.

Design of a Lower Half Body Prosthesis 10
Figure 1:Lower Half Body Prosthesis view:
The device is compact and light aiding in easy mobility of the user.

Design of a Lower Half Body Prosthesis 11
Figure 2 Prosthetic limbs and how it will operate
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.

Design of a Lower Half Body Prosthesis 12
Figure 3 Front view of prosthesis to show the different components like screws, bearings, and
parts

Design of a Lower Half Body Prosthesis 13
Figure 4 Assembly of prosthesis
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

Design of a Lower Half Body Prosthesis 14
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 ωl and the rotational velocity of the motor of the limbωm.

Design of a Lower Half Body Prosthesis 15
Figure 5 The hinge joint mechanics of the limbs
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.
¿ v
rsinα
Where ωl 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.

Design of a Lower Half Body Prosthesis 16
v= 1
2 π ωβ −S
Where ωβ −Sis the angular velocity of the ball-screw and depends on the velocity of the motor
and the gear reduction
ωm= t2
t1
ωβ−S
Combining the three equations,
ωm=ωl [ ( l
2 π ) ( 1
r . sin ( α ) ) ( t1
t2 ) ]
−1
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 (ωm) for the α was found to be 604. 84 rad/s.
The generated torque for the limb (T l) can be computed using the formula below
τl =F . r sinα
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
τ(β −s)= F .l
2 πn
Where τ(β −s)is the applied torque from the ball screw of the nut

Design of a Lower Half Body Prosthesis 17
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.
τ(β −s)=t2
t1
τm
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.
τ m=τl [ ( 2 π
l ) ( t1
t2 ) r nt .sin ( α ) ]
❑
Where nt is the overall efficiency
The nt 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.

Design of a Lower Half Body Prosthesis 18
M =3 ( n−1 )−2 f 1 −f 2
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

Design of a Lower Half Body Prosthesis 19
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

Design of a Lower Half Body Prosthesis 20
Figure 6 A simplified model of the lower limb of a human
The figure above demonstrates that 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;
θhip=θ1
θknee=θ1−θ2

Design of a Lower Half Body Prosthesis 21
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.
Figure 7 The free body diagram of the human lower limb
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

Design of a Lower Half Body Prosthesis 22
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.
Figure 8 Motion of the legs while taking a stride
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).

Design of a Lower Half Body Prosthesis 23
The figure below represents the angle between the joints of the leg , waist and the
individual segments making it up based on the reference given alongside.
Figure 9 Inclination of the foot, thigh and shank angles

Design of a Lower Half Body Prosthesis 24
Figure 10Correlation between joint angles and inclination angles of different segments
The figure demonstrates that 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 ( θthigh >θleg ¿
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.

Design of a Lower Half Body Prosthesis 25
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

Design of a Lower Half Body Prosthesis 26
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.

Design of a Lower Half Body Prosthesis 27
Bibliography
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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
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Powers, C.M., Torburn, L., Perry, J. and Ayyappa, E., 1994. Influence of prosthetic foot design
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Design of a Lower Half Body Prosthesis 28
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
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Design of a Lower Half Body Prosthesis 29
Appendices
Decision Matrices
List of Suppliers
Calculations
Numerical Analysis – Software Based
Gantt chart
Part and Assembly Drawings