This document presents the methods for a project modeling human gait using forward and inverse dynamics. It describes creating a 3-body model of the leg consisting of thigh, shank, and foot segments. Kinematic data from Winter et al. will be used to calculate joint positions, velocities and accelerations over the gait cycle. Forward dynamics will be used to model joint torques and forces during gait. Inverse dynamics will then calculate internal joint forces and stresses will be analyzed through finite element analysis. The objectives are to model both a human leg and prosthetic leg, compare their kinematics, forces and validate the results with literature to better understand discrepancies between natural and prosthetic gait.
MINIMIZATION OF METABOLIC COST OF MUSCLES BASED ON HUMAN EXOSKELETON MODELING...ijbesjournal
In this work, movement of the exoskeleton wearer and the metabolic energy changes with the assisted
devices using OpenSim platform has been attempted. Two musculoskeletal models, one with torsional ankle
spring and the other with bi-articular path spring are subjected to forward dynamic simulation.The
changes in the metabolic rate of the lower extremity muscles before and after the addition of the assistive
devices were tested. The results about the effect of these external devices on individual muscles of the lower
muscle group were analysed which provided effective results.
This paper proposes a shoulder inverse kinematics (IK) technique. Shoulder complex is comprised of the sternum, clavicle, ribs, scapula, humerus, and four joints. The shoulder complex shows specific motion pattern, such as Scapulo humeral rhythm. As a result, if a motion of the shoulder is generated without the knowledge of kinesiology, it will be seen as un-natural. The proposed technique generates motion of the shoulder complex about the orientation of the upper arm by interpolating the measurement data. The shoulder IK method allows novice animators to generate natural shoulder motions easily. As a result, this technique improves the quality of character animation.
This paper proposes a shoulder inverse kinematics (IK) technique. Shoulder complex is comprised of the
sternum, clavicle, ribs, scapula, humerus, and four joints. The shoulder complex shows specific motion
pattern, such as Scapulo humeral rhythm. As a result, if a motion of the shoulder isgenerated without the
knowledge of kinesiology, it will be seen as un-natural. The proposed technique generates motion of the
shoulder complex about the orientation of the upper arm by interpolating the measurement data. The
shoulder IK method allows novice animators to generate natural shoulder motions easily. As a result, this
technique improves the quality of character animation.
A new look at the ball disteli diagram and its relevance to knee proprioceptionWangdo Kim
Reconstruction of a torn anterior cruciate ligament (ACL) cannot be successful without a properly placed tibial tunnel. Graft impingement occurs when the graft becomes trapped in the notch between the rounded ends of the femur (intercondylar notch) with the knee in extension. A surgical technique for customizing the placement of the tibial tunnel, preventing roof impingement, is presented.
We consider the knee as a perceptual system, the units of anatomy in which are not the units of function. We are particularly interested in measuring of our knee proprioception, and of our ability to perceive change in our position through locating the instantaneous axes of the knee (IAK) during locomotion. This geometrical “patterns” of the IAK has been shown to be essential in the rehabilitation of both ACL reconstruction and the disorders in gait-related behaviors.
We present conditions of nonimpingement graft based on the principle that the tibial tunnel can be reproducibly placed in a manner that the force on each ACL graft is therefore in involution with original system.
MINIMIZATION OF METABOLIC COST OF MUSCLES BASED ON HUMAN EXOSKELETON MODELING...ijbesjournal
In this work, movement of the exoskeleton wearer and the metabolic energy changes with the assisted
devices using OpenSim platform has been attempted. Two musculoskeletal models, one with torsional ankle
spring and the other with bi-articular path spring are subjected to forward dynamic simulation.The
changes in the metabolic rate of the lower extremity muscles before and after the addition of the assistive
devices were tested. The results about the effect of these external devices on individual muscles of the lower
muscle group were analysed which provided effective results.
This paper proposes a shoulder inverse kinematics (IK) technique. Shoulder complex is comprised of the sternum, clavicle, ribs, scapula, humerus, and four joints. The shoulder complex shows specific motion pattern, such as Scapulo humeral rhythm. As a result, if a motion of the shoulder is generated without the knowledge of kinesiology, it will be seen as un-natural. The proposed technique generates motion of the shoulder complex about the orientation of the upper arm by interpolating the measurement data. The shoulder IK method allows novice animators to generate natural shoulder motions easily. As a result, this technique improves the quality of character animation.
This paper proposes a shoulder inverse kinematics (IK) technique. Shoulder complex is comprised of the
sternum, clavicle, ribs, scapula, humerus, and four joints. The shoulder complex shows specific motion
pattern, such as Scapulo humeral rhythm. As a result, if a motion of the shoulder isgenerated without the
knowledge of kinesiology, it will be seen as un-natural. The proposed technique generates motion of the
shoulder complex about the orientation of the upper arm by interpolating the measurement data. The
shoulder IK method allows novice animators to generate natural shoulder motions easily. As a result, this
technique improves the quality of character animation.
A new look at the ball disteli diagram and its relevance to knee proprioceptionWangdo Kim
Reconstruction of a torn anterior cruciate ligament (ACL) cannot be successful without a properly placed tibial tunnel. Graft impingement occurs when the graft becomes trapped in the notch between the rounded ends of the femur (intercondylar notch) with the knee in extension. A surgical technique for customizing the placement of the tibial tunnel, preventing roof impingement, is presented.
We consider the knee as a perceptual system, the units of anatomy in which are not the units of function. We are particularly interested in measuring of our knee proprioception, and of our ability to perceive change in our position through locating the instantaneous axes of the knee (IAK) during locomotion. This geometrical “patterns” of the IAK has been shown to be essential in the rehabilitation of both ACL reconstruction and the disorders in gait-related behaviors.
We present conditions of nonimpingement graft based on the principle that the tibial tunnel can be reproducibly placed in a manner that the force on each ACL graft is therefore in involution with original system.
Study of Knee Kinematics during Walking and Running in Middle Aged MalesYogeshIJTSRD
This paper aimed to figure out knee altered kinematics and to investigate possibility of knee injury in middle aged males when performing walking and running. Twelve healthy middle aged males 45 60 years volunteered to perform walking 3 km h and running 5 km h on treadmill in the biomechanics laboratory. A set of markers were attached to specify knee landmarks of each participant, who was tracked by a 7 cameras 3D motion capture system. The marker positions were used to determine the segment coordinate system SCS for calculation of knee flexion, as well as abnormal kinematics included knee internal rotation, varus rotation and anteroposterior translation. The result showed similarity of knee altered kinematics during walking and running. The maximum of knee flexion, internal rotation and varus rotation of running were higher than walking significantly, whereas there was no significant difference inanteroposterior translation p 0.05 .The repetitive anteroposterior translation could increase the risk of knee injury, while increased varus and internal rotation have been associated with the progression of iliotibial friction syndrome. This study provides the information that middle aged males runners can use to develop running techniques. Chachchanon Poolsawat "Study of Knee Kinematics during Walking and Running in Middle-Aged Males" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd41175.pdf Paper URL: https://www.ijtsrd.comother-scientific-research-area/other/41175/study-of-knee-kinematics-during-walking-and-running-in-middleaged-males/chachchanon-poolsawat
Resolution of human arm redundancy in point tasks by synthesizing two criteriaIJMER
The human arm is kinematically redundant in the task of pointing. As a result, multiple arm
configurations can be used to complete a pointing task in which the tip of the index finger is brought to a
preselected point in a 3D space. The authors have developed a four degrees of freedom (DOF)model of the
human arm with synthesis of two redundancy resolution criteria that were developed as an analytical tool
for studying the positioning tasks. The two criteria were: (1) minimizing the angular joint displacement
(Minimal Angular Displacement - MAD) and (2) averaging the limits of the shoulder joint range (Joint
Range Availability - JRA). As part of the experimental protocol conducted with ten subjects, the kinematics
of the human arm was acquired with a motion capturing system in a 3D space. The redundant joint angles
predicted by a equally weighted model synthesizing the MAD and JRA criteria resulted with a linear
correlation with the experimental data (slope=0.88; offset=1⁰; r
2=0.52). Given the experiment protocol,
individual criterion showed weaker correlation with experimental data (MAD slope=0.57, offset=14⁰,
r
2=0.36 or JRA slope=0.84, offset=-1⁰, r
2=0.45). Solving the inverse kinematics problem of articulated
redundant serials mechanism such as a human or a robotic arm has applications in fields of human-robot
interaction and wearable robotics, ergonomics, and computer graphics animation.
Stability Analysis of Quadruped-imitating Walking Robot Based on Inverted Pen...IJERA Editor
A new kind of quadruped-imitating walking robot is designed, which is composed of a body bracket, leg
brackets and walking legs. The walking leg of the robot is comprised of a first swiveling arm, a second
swiveling arm and two striding leg rods. Each rod of the walking leg is connected by a rotary joint, and is
directly controlled by the steering gear. The walking motion is realized by two striding leg rods alternately
contacting the ground. Three assumptions are put forward according to the kinematic characteristics of the
quadruped-imitating walking robot, and then the centroid equation of the robot is established. On this basis, this
paper simplifies the striding process of the quadruped-imitating walking robot into an inverted pendulum model
with a constant fulcrum and variable pendulum length. According to the inverted pendulum model, the stability
of the robot is not only related to its centroid position, but also related to its centroid velocity. Takes two typical
movement cases for example, such as walking on flat ground and climbing the vertical obstacle, the centroid
position, velocity curves of the inverted pendulum model are obtained by MATLAB simulations. The results
show that the quadruped-imitating walking robot is stable when walking on flat ground. In the process of
climbing the vertical obstacle, the robot also can maintain certain stability through real-time control adjusted by
the steering gears.
Final Project - Designing Mechatronic Systems for Rehabilitation.
With the progressively ageing of the population, the proportion of elders is strongly increasing. Linked to this stage of life are the many physical impairments that arise due to an increased frailty caused by disease or simply by the wear of body parts. In the following pages, we will study some of the most important organs and systems associated with balance maintenance. And, when not working properly, they may lead to injury or premature deaths.
Sorbonne Université - 5th Year - 1st Semester - Mechatronic Systems for Rehabilitation.
“Relationship of Kinematic Variables with the Performance of Standing Broad J...IOSR Journals
Abstract: The purpose of investigation was to study the relationship of kinematics variables with the
performance of standing broad jump. Subjects were randomly selected from J.N.V. University, Jodhpur and
M.D.S. University, Ajmer. The criterion measure used for this study was the performance in standing broad
jump and selected kinematics variables. To analyze the raw data coefficient of correlation (r) were calculated
and results were compared with the help of Analysis of variance (ANOVA) technique where level of significance
was set at .05.
ANKLE MUSCLE SYNERGIES FOR SMOOTH PEDAL OPERATION UNDER VARIOUS LOWER-LIMB PO...csandit
A study on muscle synergy of ankle joint motion is important since the acceleration operation
results in automobile acceleration. It is necessary to understanding the characteristics of ankle
muscle synergies to define the appropriate specification of pedals, especially for the accelerator
pedal. Although the biarticular muscle (i.e., gastrocnemius) plays an important role for the
ankle joint motion, it is not well understood yet. In this paper, the effect of knee joint angle and
the role of biarticular muscle for pedal operation are investigated. Experiments of the pedal
operation were performed to evaluate the muscle synergies for the ankle plantar flexion motion
(i.e., the pedal operation motion) in the driving position. The experimental results suggest that
the muscle activity level of gastrocnemius varies with respect the knee joint angle, and smooth
pedal operation is realized by the appropriate muscle synergies.
Towards Restoring Locomotion for Paraplegics: Realizing Dynamically Stable Wa...Emisor Digital
A research original from Thomas Gurriet, Sylvain Finet, Guilhem Boeris, Alexis Duburcq, Ayonga Hereid, Omar Harib, Matthieu Masselin, Jessy Grizzle and Aaron D. Ames
Even if the BMX modality has been included in the schedule of the Olympic Games since Beijing 2008, there is a lack of scientific studies concerning this sport. According to the opinion of many trainers and experts, the start of the race is very important and both neuromuscular potential and sport technique are very relevant aspects of sport performance. The purpose of this study was to analyze the technique of three top young athletes of BMX during the starting gate in order to obtain relevant information to support their trainer’s decisions.
Best practice indicators at the sectoral level and where countries standNewClimate Institute
Sebastian Sterl from NewClimate Institute presents at COP21 on "Best practice indicators at the sectoral level and where countries stand". Tuesday, 1 December, 18.30, EU Pavilion, Room Luxemburg.
Study of Knee Kinematics during Walking and Running in Middle Aged MalesYogeshIJTSRD
This paper aimed to figure out knee altered kinematics and to investigate possibility of knee injury in middle aged males when performing walking and running. Twelve healthy middle aged males 45 60 years volunteered to perform walking 3 km h and running 5 km h on treadmill in the biomechanics laboratory. A set of markers were attached to specify knee landmarks of each participant, who was tracked by a 7 cameras 3D motion capture system. The marker positions were used to determine the segment coordinate system SCS for calculation of knee flexion, as well as abnormal kinematics included knee internal rotation, varus rotation and anteroposterior translation. The result showed similarity of knee altered kinematics during walking and running. The maximum of knee flexion, internal rotation and varus rotation of running were higher than walking significantly, whereas there was no significant difference inanteroposterior translation p 0.05 .The repetitive anteroposterior translation could increase the risk of knee injury, while increased varus and internal rotation have been associated with the progression of iliotibial friction syndrome. This study provides the information that middle aged males runners can use to develop running techniques. Chachchanon Poolsawat "Study of Knee Kinematics during Walking and Running in Middle-Aged Males" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd41175.pdf Paper URL: https://www.ijtsrd.comother-scientific-research-area/other/41175/study-of-knee-kinematics-during-walking-and-running-in-middleaged-males/chachchanon-poolsawat
Resolution of human arm redundancy in point tasks by synthesizing two criteriaIJMER
The human arm is kinematically redundant in the task of pointing. As a result, multiple arm
configurations can be used to complete a pointing task in which the tip of the index finger is brought to a
preselected point in a 3D space. The authors have developed a four degrees of freedom (DOF)model of the
human arm with synthesis of two redundancy resolution criteria that were developed as an analytical tool
for studying the positioning tasks. The two criteria were: (1) minimizing the angular joint displacement
(Minimal Angular Displacement - MAD) and (2) averaging the limits of the shoulder joint range (Joint
Range Availability - JRA). As part of the experimental protocol conducted with ten subjects, the kinematics
of the human arm was acquired with a motion capturing system in a 3D space. The redundant joint angles
predicted by a equally weighted model synthesizing the MAD and JRA criteria resulted with a linear
correlation with the experimental data (slope=0.88; offset=1⁰; r
2=0.52). Given the experiment protocol,
individual criterion showed weaker correlation with experimental data (MAD slope=0.57, offset=14⁰,
r
2=0.36 or JRA slope=0.84, offset=-1⁰, r
2=0.45). Solving the inverse kinematics problem of articulated
redundant serials mechanism such as a human or a robotic arm has applications in fields of human-robot
interaction and wearable robotics, ergonomics, and computer graphics animation.
Stability Analysis of Quadruped-imitating Walking Robot Based on Inverted Pen...IJERA Editor
A new kind of quadruped-imitating walking robot is designed, which is composed of a body bracket, leg
brackets and walking legs. The walking leg of the robot is comprised of a first swiveling arm, a second
swiveling arm and two striding leg rods. Each rod of the walking leg is connected by a rotary joint, and is
directly controlled by the steering gear. The walking motion is realized by two striding leg rods alternately
contacting the ground. Three assumptions are put forward according to the kinematic characteristics of the
quadruped-imitating walking robot, and then the centroid equation of the robot is established. On this basis, this
paper simplifies the striding process of the quadruped-imitating walking robot into an inverted pendulum model
with a constant fulcrum and variable pendulum length. According to the inverted pendulum model, the stability
of the robot is not only related to its centroid position, but also related to its centroid velocity. Takes two typical
movement cases for example, such as walking on flat ground and climbing the vertical obstacle, the centroid
position, velocity curves of the inverted pendulum model are obtained by MATLAB simulations. The results
show that the quadruped-imitating walking robot is stable when walking on flat ground. In the process of
climbing the vertical obstacle, the robot also can maintain certain stability through real-time control adjusted by
the steering gears.
Final Project - Designing Mechatronic Systems for Rehabilitation.
With the progressively ageing of the population, the proportion of elders is strongly increasing. Linked to this stage of life are the many physical impairments that arise due to an increased frailty caused by disease or simply by the wear of body parts. In the following pages, we will study some of the most important organs and systems associated with balance maintenance. And, when not working properly, they may lead to injury or premature deaths.
Sorbonne Université - 5th Year - 1st Semester - Mechatronic Systems for Rehabilitation.
“Relationship of Kinematic Variables with the Performance of Standing Broad J...IOSR Journals
Abstract: The purpose of investigation was to study the relationship of kinematics variables with the
performance of standing broad jump. Subjects were randomly selected from J.N.V. University, Jodhpur and
M.D.S. University, Ajmer. The criterion measure used for this study was the performance in standing broad
jump and selected kinematics variables. To analyze the raw data coefficient of correlation (r) were calculated
and results were compared with the help of Analysis of variance (ANOVA) technique where level of significance
was set at .05.
ANKLE MUSCLE SYNERGIES FOR SMOOTH PEDAL OPERATION UNDER VARIOUS LOWER-LIMB PO...csandit
A study on muscle synergy of ankle joint motion is important since the acceleration operation
results in automobile acceleration. It is necessary to understanding the characteristics of ankle
muscle synergies to define the appropriate specification of pedals, especially for the accelerator
pedal. Although the biarticular muscle (i.e., gastrocnemius) plays an important role for the
ankle joint motion, it is not well understood yet. In this paper, the effect of knee joint angle and
the role of biarticular muscle for pedal operation are investigated. Experiments of the pedal
operation were performed to evaluate the muscle synergies for the ankle plantar flexion motion
(i.e., the pedal operation motion) in the driving position. The experimental results suggest that
the muscle activity level of gastrocnemius varies with respect the knee joint angle, and smooth
pedal operation is realized by the appropriate muscle synergies.
Towards Restoring Locomotion for Paraplegics: Realizing Dynamically Stable Wa...Emisor Digital
A research original from Thomas Gurriet, Sylvain Finet, Guilhem Boeris, Alexis Duburcq, Ayonga Hereid, Omar Harib, Matthieu Masselin, Jessy Grizzle and Aaron D. Ames
Even if the BMX modality has been included in the schedule of the Olympic Games since Beijing 2008, there is a lack of scientific studies concerning this sport. According to the opinion of many trainers and experts, the start of the race is very important and both neuromuscular potential and sport technique are very relevant aspects of sport performance. The purpose of this study was to analyze the technique of three top young athletes of BMX during the starting gate in order to obtain relevant information to support their trainer’s decisions.
Best practice indicators at the sectoral level and where countries standNewClimate Institute
Sebastian Sterl from NewClimate Institute presents at COP21 on "Best practice indicators at the sectoral level and where countries stand". Tuesday, 1 December, 18.30, EU Pavilion, Room Luxemburg.
[ITOnAir] 데브멘토 동영상, 배성환 LG전자 과장 2/2부_성공하는 모바일 서비스를 위한 실전 강연
고객이 더 스마트해진 이유그리고 우리가 스마트한 고객을 이해하기 위해 시장을 어떻게 바라봐야 하는가?또 어떤 전략을 통해 대응할 수 있을까?본 영상은 데브멘토 ITOnAir (tv.devmento.co.kr) 또는 다음tv팟(tvpot.daum.net/pot/Itonair)을 통해 웹과 모바일로 시청하실 수 있습니다.
Universal Health Coverage (UHC) Day 12.12.14, NepalDeepak Karki
This presentation is made on the first ever Universal Health Coverage (UHC) Day 12.12.14 celebration in Nepal by Nepal Health Economics Association (NHEA).
This is a team presentation, we presented, of our analysis on the "Channel Tunnel" (Euro tunnel) project, as our term project for the course "International Project Management & Professional Responsibility" of "Project Management" program.
[ITOnAir] 데브멘토 동영상, 배형미 스마트비즈랩 대표_성공하는 모바일 서비스를 위한 실전 강연
협업과 UI/UX, 스토리와 UX발전이 없으면 비전도 없다인생은 누가 더 대단한 이야기를 갖고 있는가의 싸움협업(Collaboration)과 협력(Cooperation)의 차이본 영상은 데브멘토 ITOnAir (tv.devmento.co.kr) 또는 다음tv팟(tvpot.daum.net/pot/Itonair)을 통해 웹과 모바일로 시청하실 수 있습니다.
These slides were presented by Heila Lotz-Sisitka, T-LEARNING network lead and Professor in Education at Rhodes University, South Africa, as part of an ISSC webinar on transformative knowledge for sustainability. Find out more about the Transformations to Sustainability programme and watch the webinar here:http://www.worldsocialscience.org/2016/06/webinar-transformative-knowledge-networks-solutions-oriented-research-practice/
Austin Journal of Robotics & Automation is an international scholarly, peer review, Open Access journal, initiated with an aim to promote the research in Robotics & Automation, which deals with design, construction, operation, and application of robots.
Austin Journal of Robotics & Automation is a comprehensive Open Access peer reviewed scientific journal that covers multidisciplinary fields. We provide limitless access towards accessing our literature hub with colossal range of articles. The journal aims to publish high quality varied article types such as Research, Review, Short Communications, Case Reports, Perspectives (Editorials).
Austin Journal of Robotics & Automation supports the scientific modernization and enrichment in Robotics & Automation research community by magnifying access to peer reviewed scientific literary works. Austin Publishing Group also brings universally peer reviewed member journals under one roof thereby promoting knowledge sharing, collaborative and promotion of multidisciplinary technology.
Ik analysis for the hip simulator using the open sim simulatorEditorIJAERD
The model of the project to create a detailed assembly of muscles spotting the hip joint. Additional muscles
and combinations were added to the baseline lower extremity assemblies currently available in OpenSim. The geometry
of the muscles was adjusted to pair moment arms reported here. The slack moment and the isometric were added to the
arithmetic value of the tanquntial assembly of joints
Dynamic Model of Hip and Ankle Joints Loading during Working with a Motorized...J. Agricultural Machinery
The main objective of this paper is to develop a seven-link dynamic model of the operator’s body while working with a motorized backpack sprayer. This model includes the coordinates of the sprayer relative to the body, the rotational inertia of the sprayer, the muscle moments acting on the joints, and a kinematic coupling that keeps the body balanced between the two legs. The constraint functions were determined and the non-linear differential equations of motion were derived using Lagrangian equations. The results show that undesirable fluctuations in the ankle force are noticeable at the beginning and end of a swing phase. Therefore, injuries to the ankle joint are more likely due to vibrations. The effects of engine speed and sprayer mass on the hip and ankle joint forces were then investigated. It is found that the engine speed and sprayer mass have significant effects on the hip and ankle forces and can be used as effective control parameters. The results of the analysis also show that increasing the engine speed increases the frequency of the hip joint force. However, no significant effects on the frequency of the ankle joint force are observed. The results of this study may provide researchers with insight into estimating the allowable working hours with the motorized backpack sprayers, prosthesis design, and load calculations of hip implants in the future.
Robotic Leg Design to Analysis the Human Leg Swing from Motion CapturejournalBEEI
In this paper presented the prototype of robotic leg has been designed, constructed and controlled. These prototype are designed from a geometric of human leg model with three joints moving in 2D plane. Robot has three degree of freedom using DC servo motor as a joint actuators: hip, knee and ankle. The mechanical leg constructed using aluminum alloy and acrylic material. The control movement of this system is based on motion capture data stored on a personal computer. The motions are recorded with a camera by use of a marker-based to track movement of human leg. Propose of this paper is design of robotic leg to present the analysis of motion of the human leg swing and to testing the system ability to create the movement from motion capture. The results of this study show that the design of robotic leg was capable for practical use of the human leg motion analysis. The accuracy of orientation angles of joints shows the average error on hip is 1.46º, knee is 1.66º, and ankle is 0.46º. In this research suggesting that the construction of mechanic is an important role in the stabilization of the movement sequence.
Lower Limb Musculoskeletal Modeling for Standing and Sitting Event by using M...ijsrd.com
This paper shows how the musculoskeletal modeling for standing and sitting event of lower limb of humans is possible using MSMS (Musculoskeletal Modeling Software). Concept, significance and factors of musculoskeletal modeling of lower limb have been detailed. It presents how the complexity of biomechanics related to lower limb can modeled with MSMS and also represents how such model can be useful in generating MATLAB/SIMULINK ® model that can be further used in the development of prototype neuroprosthesis model for paraplegic patients having lower extremity disorders. Proposed modeling includes 12 leg virtual muscles which shows its accuracy for event of standing to sitting event with due consideration of the coordinating position, Mass, Inertia used for rigid body segment, and Joint Type, Translational Axes, Rotational Axes used for lower limb joints. The result generated by MSMS for proposed modeling has been presented. Merits and demerits of proposed modeling have also been discussed.
Crimson Publishers- The Effect of Medial Hamstring Weakness on Soft Tissue Lo...CrimsonPublishers-SBB
Anterior cruciate ligament (ACL) reconstructions are frequently performed in the United States of America. The medial hamstrings graft has been shown to produce lower rates of osteoarthritis (OA) than the patellar tendon graft. The goal of this study was to determine how altering medial hamstring strength during surgery affects soft tissue loading, and hence the joint’s proclivity towards OA. Muscle-actuated forward dynamic simulations of running were performed for normal muscle strength and decreased medial hamstring strength. The results show weakening the medial hamstrings caused an overall decrease in total hamstrings force by 7%, in total quadriceps force by 35%, and in cartilage contact force by 6%. This decreased force may be protective against long-term OA.
2. December 6, 2016
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Table of Contents
Section Page Number
Introduction and Objectives 2
Methods 5
Forward Dynamics 10
Kinematics 11
Equations of Motion 15
Constraints 16
Inverse Dynamics 19
Prosthetics Implementation 31
Results 35
Conclusion 44
References 45
Appendices 46
Appendix 1: Kinematics Equations 46
Appendix 2: Equations of Motion 50
Appendix 3: Matlab Code – Kinematics and EoMs 51
Appendix 4: Matlab Code – Constraints 56
Appendix 5: Matlab Code – Inverse Dynamics 58
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INTRODUCTION AND OBJECTIVES
Background
There are an estimated 1.9 million amputees in the United States and approximately 185,000 amputations
surgeries performed each year. With an aging population, this number is likely to rise due to the fact that
the majority of amputations result from peripheral Vascular Disease and Diabetes. Many of these
individuals opt to use a prosthetic device to assist with the functions of daily living. However, current state
of the art in the limb replacement industry cannot match the functionality of a human limb.
Transfemoral amputees (those who lose their leg above the knee, across the femur) who use a prosthetic
leg must use approximately 80% more energy to walk than a person with two whole legs. Due to this, it
can be very difficult for transfemoral amputees to regain normal movement. Although many newer
transfemoral prosthetic legs have improved functionality by use of motors and computer
microprocessors, these devices are costly, and many continue to use simpler, more cumbersome designs.
Human Gait
“Gait” is defined by Merriam-Webster as, “a manner of walking on foot”. Human gait has been studied
abundantly for a multitude of applications for a better understanding of human movement. It is for this
reason that a simulation of human gait was chosen as an appropriate means by which to assess the
kinematics and forces associated with the human leg. See Figure 1 below for a diagram of the human gait
cycle.
Figure 1: Complete human gait cycle shown in the anatomic sagittal plane
As shown in the above diagram, there are two phases to the gait cycle for each leg: the Stance Phase, the
portion during which the foot is in contact with the walking surface, and the Swing Phase, the portion of
the gait cycle during which the foot has no contact with the ground. Throughout this report, start time (to
= 0 seconds) is defined at the moment of ‘Toe Off’ of the right leg.
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Anatomic Definitions
Throughout this report, references are made using standard anatomic definitions.
There are three anatomic reference planes, used to describe body motion and positioning. These include
the Sagittal Plane, in the anterior-posterior direction, the Transverse Plane, in the distal-proximal
direction, and the Frontal Plane, in the medial-lateral direction. See Figure 2 below for a visual
representation of these planes.
Figure 2: Anatomic reference frames
Purpose
The purpose of this study is to conduct both forward and inverse dynamics analysis of a human leg and
prosthetic leg for comparison of kinematics, internal forces, and external forces using gait cycle data. The
results of this study may provide a means by which a comparison of the functionality of a transfemoral
prosthetic leg and a human leg may be achieved. It is our hope that an analysis of the dynamics of both
systems might create a clearer understanding of gait and functionality discrepancies between an artificial
and human leg in order to improve prosthetic leg design.
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Objectives
The objectives of this study are outlined below:
● Create a means by which to solve for the forward dynamics of a human leg and prosthetic leg.
This includes the kinematics and equations of motion with constraints for each.
● Create a model for analysis for both a human leg and prosthetic leg. This will provide information
about inverse dynamics, including internal forces, as well as stress analysis through finite element
analysis (FEA).
● Validate solutions with existing literature.
● Assess the similarities and differences in the solutions found in the dynamics of the human leg
and prosthetic leg.
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METHODS
Defining the Model
For the purposes of this project, in an effort to analyze the most ‘average’ circumstances for human lower
limb dynamics, the leg model is based off 50th
percentile adult male anthropometric data in regards to
height, weight, leg segment lengths, and leg segment masses. The 50th percentile adult male weighs 75
kg.
The following Figure 3 shows 50th
percentile anthropometric data for height and limb length segments.
These were used in the segment lengths of the model.
Figure 3: Anthropometric data for the 50th
percentile male for height and limb segment lengths.
The following figure illustrates the model to be used in the multibody dynamics.
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Figure 4: Diagram of human leg for forward dynamics analysis, including reference and local coordinate
systems.
As shown in Figure 4, the human leg is modelled as a 3-body system (thigh, shank, and foot: Body 1, Body
2, and Body 3, respectively) with local coordinate systems at each joint (hip, knee, and ankle). Each local
coordinate system aligns the 𝑛1
𝑘
axis with the line of action of the leg segment, the 𝑛2
𝑘
is perpendicular to
axis 𝑛1
𝑘
, rotated 90° in the positive (counterclockwise) direction from 𝑛1
𝑘
. Axis 𝑛3
𝑘
is aligned in the medial-
lateral orientation of the system (out of the page). Each system also has a reference coordinate system,
O, shown in yellow in the above figure.
The gait movement is restricted to the sagittal plane and, assuming symmetry, it is only required to
conduct a simulation and model with just one leg. The right leg will be used in this study.
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Data
Winter, et al. have published a complete data set for the gait cycle including information for each leg
segment and joint in regards to their position, angular velocities, and angular accelerations through the
gait cycle. This set is used as the definitive data for the project.
As an alternative, the software program Quintic Biomechanic is a biomechanics computational software
that derives data from a video using motion capture. The program is then able to export kinematic data
as well as force data. Without the full version, we were unable to simulate walking and gather data from
the program. See the images below for a sample output from Quintic Biomechanic trial software as a
proof of concept for potential implementation in the future for data harvesting. This could also be used
to measure the gait cycle of an individual with a lower limb prosthetic. This would make computations for
forward and inverse dynamics possible for the prosthetic scenario that we were unable to accomplish
without such data.
Figure M.4.1: vector representation of limb segments of an individual recorded running. The blue and
yellow identify the foot. The green identifies the shank. The red identifies the thigh.
The following are sample data outputs from the Quintic Biomechanic softwawre for a walking individual.
The first is kinematic data for the hip joint, then the knee, and last the ankle.
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Figure M.4.2: Distance, Velocity, and Acceleration data for the Hip recorded with motion capture during
walking.
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Figure M.4.3: Distance, Velocity, and Acceleration data for the Knee recorded with motion capture
during walking.
Figure M.4.4: Distance, Velocity, and Acceleration data for the Ankle recorded with motion capture
during walking.
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FORWARD DYNAMICS
System
For the simplification of the system, each body of the anatomical right leg (shown previously in Figure 4)
is represented by a link segment with masses of each concentrated at the center of mass and moments
of inertia for each segment acting about the center of mass. Local limb coordinates are as shown in the
previous Figure 5.
Figure 5: Simplified human led diagram for modeling. Blue rotation arrows (positive direction) are
indicated about the hip, knee, and ankle joints.
Masses for each are calculated based on a percentage of total body mass for the 50th percentile male as
are the moments of inertia. Joints are represented as hinge joints, rotating about only the n3 coordinate
axis.
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KINEMATICS
Equations
There are three bodies in the system: the thigh, the shank, and the foot. Because each joint only allows
for rotation about a single axis, the number of degrees of freedom of this system is 3.
The generalized coordinates of the system are presented below in equations (1) and (2). The associated
position vectors and skew matrices for each body are shown in equations (3) through (7).
{𝑥} = [0 0 𝑥3 0 0 𝑥6 0 0 𝑥9] = [0 0 𝜃1 0 0 𝜃2 0 0 𝜃3] (1)
{𝑥̇} = [0 0 𝑥̇3 0 0 𝑥̇6 0 0 𝑥̇9] = [0 0 𝜃̇1 0 0 𝜃̇2 0 0 𝜃̇3] (2)
𝑞⃑1 = 𝜉 ≅ 0 (3)
𝑞⃑ 𝑘 = [𝑙 𝑘 0 0] 𝑇
(4)
𝑆 𝑞𝑘 = 𝑙 𝑘 [
0 0 0
0 0 −1
0 1 0
] (5)
𝑟⃑𝑘 = [
𝑙 𝑘
2
0 0]
𝑇
(6)
𝑆𝑟1 =
𝑙1
2
[
0 0 0
0 0 −1
0 1 0
] (7)
The shifter matrices between each of the bodies are all the same, shown by equation (8). This is due to
the fact that they rotate about the same parallel axes at each joint.
The shifter matrices for bodies 2 and 3 with respect to the global coordinate system are calculated as
shown in equations (9) and (10).
𝑆 𝑘,𝑘−1
= [
cos(𝜃 𝑘) sin(𝜃 𝑘) 0
−sin(𝜃 𝑘) cos(𝜃 𝑘) 0
0 0 1
] (8)
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The time derivatives of the shifter matrices are displayed in equations (11), (12), and (13) accordingly.
𝑆̇10
= [
−sin(𝜃1) cos(𝜃1) 0
−cos(𝜃1) −sin(𝜃1) 0
0 0 0
] ∗ 𝜃̇1 (11)
𝑆̇20
= [
−sin(𝜃1 + 𝜃2) cos(𝜃1 + 𝜃2) 0
−cos(𝜃1 + 𝜃2) −sin(𝜃1 + 𝜃2) 0
0 0 0
] ∗ (𝜃̇1 + 𝜃̇2) (12)
𝑆̇30
= [
−sin(𝜃1 + 𝜃2 + 𝜃3) cos(𝜃1 + 𝜃2 + 𝜃3) 0
−cos(𝜃1 + 𝜃2 + 𝜃3) −sin(𝜃1 + 𝜃2 + 𝜃3) 0
0 0 0
] ∗ (𝜃̇1 + 𝜃̇2 + 𝜃̇3) (13)
The angular velocity and acceleration of each body is calculated by the following equations (14 and 15).
𝜔̅ 𝑘
= {𝑥̇} 𝑇[𝜔 𝑘]{𝑛̅} (14)
𝛼̅ 𝑘
= (({𝑥̈} 𝑇[𝜔 𝑘] + {𝑥̇} 𝑇[𝜔 𝑘])){𝑛̅} (15)
Partial angular velocities and their respective time derivatives of each body is shown in the equations
below (16 and 17).
Body 1 Body 2 Body 3
Partial Angular Velocity [𝜔1] = [
𝐼
03𝑥3
03𝑥3
] [𝜔2] = [
𝐼
𝑆10
03𝑥3
] [𝜔3] = [
𝐼
𝑆10
𝑆20
] (16)
Time Derivative of
Partial Angular Velocity
[𝜔̇ 1] = [
03𝑥3
03𝑥3
03𝑥3
] [𝜔̇ 2] = [
03𝑥3
𝑆̇10
03𝑥3
] [𝜔̇ 3] = [
03𝑥3
𝑆̇10
𝑆̇20
] (17)
𝑆20
= 𝑆21
∗ 𝑆10
= [
cos(𝜃1 + 𝜃2) sin(𝜃1 + 𝜃2) 0
−sin(𝜃1 + 𝜃2) cos(𝜃1 + 𝜃2) 0
0 0 1
] (9)
𝑆30
= 𝑆32
∗ 𝑆21
∗ 𝑆10
= [
cos(𝜃1 + 𝜃2 + 𝜃3) sin(𝜃1 + 𝜃2 + 𝜃3) 0
−sin(𝜃1 + 𝜃2 + 𝜃3) cos(𝜃1 + 𝜃2 + 𝜃3) 0
0 0 1
] (10)
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In order to determine the mass-center velocity acceleration of each segment, generalized coordinates
were utilized. See equation (18).
{𝑦} 𝑇
= [0 0 𝜃̇1 0 0 (𝜃̇1 + 𝜃̇2) 0 0 (𝜃̇1 + 𝜃̇2 + 𝜃̇3)] (18)
where the Gimball matrix is shown in equation (19).
[𝐼̂] = [
0 0 0
0 0 0
0 0 1
] [𝑊] = [
𝐼̂ 𝐼̂ 𝐼̂
0 𝐼̂ 𝐼̂
0 0 𝐼̂
] (19)
The mass center velocity of the thigh, shank, and foot is calculated by use of equation (21).
𝑣̅ = {𝑥̇} 𝑇[𝑤][𝑉]{𝑛̅} (20)
Lastly, the associated mass center velocity for each body is calculated by the following formula
𝑎̅𝑗 =
𝑑
𝑑𝑡
𝑣̅𝑗 = ({𝜉̈1} 𝑇
+ {𝑦̇} 𝑇[𝑉 𝐽] + {𝑦} 𝑇
[𝑉̇ 𝐽
]){𝑛̅} (21)
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Solutions
The numerical results of forward dynamics are calculated via the Matlab program (Appendix 3), utilizing
all of the kinematics relationships listed above. The code requests a time input from the user, pulls data
from the Winter et al. data file, and outputs kinematics solutions as well as a figure visually displaying a
graphical image representation of the orientation of the leg segments at the specified moment in time.
See Figure 6 below.
Figure 6: Figure output of Matlab code graphically displays representation of system orientation at a
specified moment in time
SolidWorks
The computer-aided design (CAD) software, SolidWorks, was used to model a human leg with the same
parameters as those used in the Matlab computation of the kinematics. A prescribed motion path was
applied to the leg model in order to simulate the gait cycle using angular velocities at each joint over time.
This then allowed for collection of kinematics data. This data is presented in the results section. The
following figure is an image of the CAD model developed for the human right leg.
Figure 7: CAD model of a human right leg
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EQUATIONS OF MOTION
The general Equation of Motion is defined by the following equation (21),
𝑎𝑥̈ + 𝑏𝑥̇ + 𝑐𝑥̇ = 𝑓 (21)
where matrices [a], [b], [c], {f}, { 𝑥̇}, and { 𝑥̈} are defined in equations (22) through (29),
{𝑥̇} = [0 0 𝜃̇1 0 0 𝜃̇2 0 0 𝜃̇3]
{𝑥̈} = [0 0 𝜃1
̈ 0 0 𝜃2
̈ 0 0 𝜃3
̈ ]
(22)
(23)
The [a] is calculated as with equation (24),
[𝑎] = ∑ 𝑚 𝑘 [𝑉𝑤] 𝑘
[𝑉𝑤
𝑘
] 𝑇
+ ∑[𝑤 𝑘
] [𝐼 𝑜𝑘][𝑤 𝑘
] 𝑇 (24)
where mk is the mass of each body and [𝐼 𝑜𝑘] is the moment inertia obtained from data presented in de
Leva’s paper.
[𝑉𝑤
𝑘
]3𝑛×3 = [𝑊]3𝑛×3[𝑉 𝑘
]3𝑛×3 (25)
The Gimball matrix [W] is demonstrated in equation (19). Using the [𝑉𝑤
𝑘
] obtained for [a], [b] is computed
as with the following equation (26),
[𝑏] = ∑ 𝑚 𝑘 [𝑉𝑤] 𝑘
[𝑉𝑤
̇ 𝑘
] 𝑇
+ ∑[𝑤 𝑘
] [𝐼 𝑜𝑘][𝑤̇ 𝑘
] 𝑇 (26)
The [c] matrix is obtained from the following equation (27),
[𝑐] = ∑[𝑤 𝑘
] [Ω 𝑥
𝑜𝑘
][𝐼 𝑜𝑘][𝑤 𝑘
] 𝑇 (27)
where
[Ω 𝑥
𝑜𝑘
]=[S 𝑜𝑘
̇ ] [S 𝑘𝑜] (28)
Finally, the equation of motion is computed as,
[𝑓] = [𝑉𝑤
𝑘
]{𝑓𝑘} + ∑[𝑤 𝑘
] [𝑀 𝑘] (29)
Where,
{𝑓1} = [0 − 𝑚1 𝑔 0] 𝑇
{𝑓2} = [0 − 𝑚2 𝑔 0] 𝑇
{𝑓3} = [0 − 𝑚3 𝑔 0] 𝑇
(30)
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CONSTRAINTS
Prescribed Motion
Knee and ankle motion is well defined during a standard gait cycle, and can be related by x and y-
coordinates in a global coordinate system. See Chart 1 below for the Winter et al. data plotted for both
the knee and ankle x and y-positions for one complete gait cycle,
Chart 1: X and Y position data for the right leg knee and ankle for one complete gait cycle, indicating
position locations of ‘Toe Off’ to ‘Heel Strike’.
As you can see, the knee is further advance in the x-direction at the time of toe-off. This explains the
forward-shifted knee positioning chart as compared to the heel position data. See graphical image below
for a rendering of the Matlab positioning output figure overlaid onto the same chart as above.
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Figure 8: Matlab positioning output overlaid on Winter x-y gait cycle position data as a visual
representation.
The Winter et al. data for joint angular velocities is inputted into the SolidWorks software model to
simulate the motion path of the leg.
If one were to constrain a body to behave as a human leg during gait, an equation relating the x and y
position coordinates for the knee and ankle in Chart 1 would be required. However, it is not possible to
derive a relationship without breaking the data into small sections or over-simplifying the motion. As an
example proof of concept for constraining the system with prescribed motion, a three-body system is
constrained both by a constant speed and a straight line path. See Appendix 4 for the computational
Matlab code.
Prescribed Motion – Constant Speed and Straight Line
The equations for a constrained multibody system are given by:
𝑓∗
+ 𝑓 + 𝐵 𝑇
𝜆 = 0 (31)
Then the T matrix is resolved in a way that constraint forces are equal to zero:
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𝑇𝑓∗
+ 𝑇𝑓 = 0
𝜃̇1 + 𝜃̇2 + 𝜃̇3 = 0
𝑟𝑎𝑑
𝑠𝑒𝑐
(32)
(33)
We could define the following constraint for an end effector:
𝑦1𝑐 = 2𝑡 (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑠𝑝𝑒𝑒𝑑)
𝑥13 = 0.5 (𝑓𝑜𝑙𝑙𝑜𝑤 𝑎 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑙𝑖𝑛𝑒)
(34)
(35)
Differentiation of the above yields:
or
Where:
Initial Condition:
According to the figure below our initial conditions will be:
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INVERSE DYNAMICS
Free Body Diagram
Using the free body diagram (FBD) shown below in Figure 9, internal forces of the human leg can be
calculated.
Figure 9: Free body diagram of the human right leg, derived from the previously defined system. Green
arrows indicate joint moments, purple arrows indicate external forces, and blue arrows identify internal
forces between joints. The global coordinate system (O) is shown in yellow.
R1
R1
R2
R2
R2
R2
R3
R3
R3
R3
𝑛ሬ⃑1
𝑛ሬ⃑2
𝑛ሬ⃑3
O
Body 1
I1 m1
m1
g
Mhip
Mknee
I2 m2
Body
2
m2g
Mknee
Mankle
Mankle
Body
3
I3
m
3
m3
g
Fy,ground
Fx,ground
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Many values listed in Figure 9 are already known about the system. The angular accelerations can be
pulled from the Winter et al. data, as well as the angles at each joint. Linear acceleration values in the x
and y direction of the center of masses were found during kinematics calculations. The mass of the
segments, distance from the joints to the center of masses, and moments of inertia about the mass
centers are found using scaling of the 50th
percentile male anthropometric data. This is essential for all
inverse dynamics calculations.
Internal forces form equal and opposite reaction forces. Therefore, when one is solved for, the other can
be found. For example, the internal forces applied by the shank on the knee are equal and opposite to
those applied by the thigh on the knee. This is important because it easily reduces the number of unknown
values.
The two Fground forces in Figure 9 are ground reaction forces. In order to measure the force exerted by the
body on an external body or load, we need a suitable force-measuring device. Such a device, called a force
transducer, gives an electrical signal proportional to the applied force. Ground reaction forces, acting on
a foot during standing, walking or running, are traditionally measured by force plates. Force plate output
data provides us with ground reaction force vector components: vertical load plus two shear loads acting
along the force plate surface, that are usually resolved into anterior – posterior and medial – lateral
directions. The following figure shows a schematic of a force plate.
Figure 10: Traditional force plate schematic, used to measure ground reaction forces during gait.
The following figure represents an example of the characteristic curve for the ground reaction force in the
y-direction during the stance phase of the gait cycle. In modelling of the right leg, no ground reaction force
is present during the swing phase of the gait cycle.
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Figure 11: Ground reaction force during the stance phase of the gait cycle, normalized as a percentage
of body weight
The highest ground reaction forces in the vertical direction occur during heel strike and just before toe
off, as indicated in Figure 11. These are the points of highest pressure, due to lowest surface area. During
heel strike, only the heel is supporting the body, and just before toe off, the distal end of the foot is
supporting the body. During both of these instances, the ground reaction force exceeds the total body
weight.
Please note that the ground reaction forces change as a function of the position of the foot during the gait
cycle, meaning that the Fground force locations in the FBD are arbitrary until the portion of the gait cycle of
interest is determined.
SIMM
The ground reaction force data used for this project was derived from the SIMM software, having applied
the same parameters and gait data as the previously completed kinematics of the system. SIMM is a
biomechanics simulation software tool. This software was utilized for this project for the creation of a gait
analysis test. This was then used for the measurement of ground reaction forces during typical gait. The
software allows for parameter inputs, such as body weight and walking speed. The reaction forces
measured by SIMM software are nothing more than the algebraic summation of all body segments mass-
acceleration products. See Figure 12 below for a graphical representation of the output of the SIMM
program for ground reaction force measurement, from heel contact to toe off.
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Figure 12: SIMM model of ground force reaction measurement with a force plate. Green arrows show
direction and magnitude of the ground reaction force on the leg.
The following are the SIMM outputs for the ground reaction forces in the x, y, and z-directions from the
force plate measurement. Vertical lines represent gait cycle landmarks.
Figure 13: SIMM Ground Reaction Force output in the x-direction
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Figure 14: SIMM Ground Reaction Force output in the y-direction
Figure 14: SIMM Ground Reaction Force output in the z-direction
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Figure 16: SIMM Ground Reaction Force output in the x, y, and z-directions. The blue line represents the
vertical ground reaction force, and the red and green represent shear forces in the x and y directions
respectively.
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Reaction Forces at Ankle
Internal forces and the moment at the ankle can be found using the following free body diagram:
Figure 17: Free body diagram of the human foot from Figure 9. Orange arrows are added to indicate
linear and angular accelerations.
Based on the FBD of the foot and Newton’s Second Law (𝐹 = 𝑚 ∗ 𝑎) and known values found previously,
values for the reaction forces (R) can be found. First, for the knee, reaction forces R2x and R2y can be
calculated. The reaction force at the ankle in the x-direction is as follows:
∑ 𝐹𝑥 = 𝑚𝑎 𝑥
𝑅3𝑥 + 𝐹𝑥,𝑔𝑟𝑜𝑢𝑛𝑑 = 𝑚3 𝑎3𝑥
The reaction force at the ankle in the y-direction is as follows:
∑ 𝐹𝑦 = 𝑚𝑎 𝑦
𝑅3𝑦 + 𝐹𝑦,𝑔𝑟𝑜𝑢𝑛𝑑 − 𝑚3 𝑔 = 𝑚3 𝑎3𝑦
The moment about the ankle, Mankle can be also be found using the FBD above. The following is the
calculation for the angle θ in Figure 17:
𝜃 = 180 − 𝜃ℎ𝑖𝑝 + 𝜃 𝑘𝑛𝑒𝑒 + 𝜃 𝑎𝑛𝑘𝑙𝑒
The moment about the ankle, Mankle can be also be found using the following equation for sum of moments
at a joint. The term lCOM is defined as the distance to the center of mass of the foot from the point of action
of the force within its mathematical argument:
∑ 𝑀 = 𝐼𝛼
𝑀 𝑎𝑛𝑘𝑙𝑒 + 𝐹𝑦,𝑔𝑟𝑜𝑢𝑛𝑑 × 𝑙 𝐶𝑂𝑀 + 𝐹𝑥,𝑔𝑟𝑜𝑢𝑛𝑑 × 𝑙 𝐶𝑂𝑀 − 𝑅3𝑦 × 𝑙 𝐶𝑂𝑀 ∗ cos(θ) − 𝑅3𝑥 × 𝑙 𝐶𝑂𝑀 ∗ sin(θ) = 𝐼3 𝛼3
R3
R3
Body 3
I3
m
3
m3
g
Mankle
Fy,ground
Fx,ground
a3
a3
α3
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Reaction Forces at the Knee
Internal forces and the moment at the knee can be found using the following free body diagram:
Figure 18: Free body diagram of the human leg shank from Figure 9. Orange arrows are added to
indicate linear and angular accelerations.
Based on the FBD of the shank and Newton’s Second Law (𝐹 = 𝑚 ∗ 𝑎) and known values found previously,
values for the reaction forces (R) can be found. For the knee, reaction forces R2x and R2y can be calculated.
The reaction force at the knee in the x-direction is as follows:
∑ 𝐹𝑥 = 𝑚𝑎 𝑥
𝑅2𝑥 = 𝑚2 𝑎2𝑥
The reaction force at the knee in the y-direction is as follows:
∑ 𝐹𝑦 = 𝑚𝑎 𝑦
𝑅2𝑦 = 𝑚2 𝑎2𝑦
The moment about the knee, Mknee can be also be found using the FBD above. The following is the
calculation for the angle θ in Figure 18:
θ = 90° − θℎ𝑖𝑝 − θ 𝑘𝑛𝑒𝑒
Body 2
R2
R2
R3
R3
I2
m2
m2g
Mknee
Mankle
a2
a2
α2
θ
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The general equation for sum of moments at a joint can be used to calculate Mknee about the center of
mass. The term lCOM is defined as the distance to the center of mass of the foot from the point of action
of the force within its mathematical argument:
∑ 𝑀 = 𝐼𝛼
𝑀 𝑘𝑛𝑒𝑒 − 𝑅 𝑥2 × 𝑙 𝐶𝑂𝑀 ∗ sin(θ) − 𝑅 𝑦2 × 𝑙 𝐶𝑂𝑀 ∗ cos(θ) = 𝐼2 𝛼2
Solutions
In order to solve for the joint internal forces and moments, it is required to know, at any given moment
during the gait cycle, the COP. SIMM provides position vector outputs for the gait cycle, calculated using
parameters listed in Figure 10 from the force plate, to meet this need. See Figures 19, 20, and 21 below:
Figure 19: x-position of the foot, measured by the force plate
Figure 20: y-position of the foot, measured by the force plate
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Figure 21: z-position of the foot, measured by the force plate. From the previous Figure 10, it is evident
that the z-position does not change throughout gait (z is about equal to 0.6 m)
With data exported for each of these position values, the COP can be found. The COP is then used to
determine the moment arm for Fx,ground and Fy,ground. Using known values from previously completed
calculations for the system and the FBD shown in Figures 17 and 18, the reaction forces can be solved for.
However, data is not available for these charts, and the COP cannot be determined with the current
software. Further, a literature search did not yield any data sets for COP during the gait cycle.
A sample Matlab code was written as if data were available for the position of the COP over time in order
to calculate the reaction forces with values calculated in the kinematics and equations of motion Matlab
code in Appendix 3. See sample Matlab code in Appendix 5.
Expected outputs for the Matlab code for the reaction forces and joint moments over the gait cycle are
as follows:
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Table 1: Ground Reaction Forces and Joint Moments over the gait cycle from Winter et al. Data
Parameter
Ground Reaction Forces
Winter et al Data, Matlab Algorithm
Ankle
Knee
-150
-50
50
150
250
350
450
550
650
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Force(Newtons)
Time (Seconds)
X Direction Y Direction
-100
0
100
200
300
400
500
600
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Forces(Newtons)
Time (Seconds)
X Direction Y Direction
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PROSTHETICS IMPLEMENTATION
STRESS ANALYSIS (FEA)
In order to apply the results of the gait analyses to a prosthetic limb, ANSYS can be used to optimize
prosthetic leg design. Using values calculated in the previous sections, a proof-of-concept ANSYS model
of a prosthetic shank was completed to complete a worst-case scenario stress analysis.
The following figure shows an example of an individual with a transfemoral prosthetic leg. The prosthetic
leg model was created in the CAD software, SolidWorks. The shank component will be assessed for
stresses by finite element analysis.
Figure 22: Multibody system showing a human with prosthetic leg.
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Using the finite element analysis (FEA) software, ANSYS, a stress analysis of the shank of a prosthetic shank
was completed with force information found previously for the human leg. First, the model is uploaded
to the software.The material for this part of prosthetic leg is Titanium.
Figure 23: prosthetic leg shank model uploaded from SolidWorks to ANSYS
Then a finite element mesh was created for the model shank.
Figure 24: Prosthetic leg shank with a finite element mesh applied
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Then, forces and moments at the joints, calculated previously in the inverse dynamics section, are
assigned and applied to the model within the ANSYS software.
Figure 25: Prosthetic leg shank model with forces and moments simulated at the joints.
Following application of forces, the deformation can be calculated. See Figure XX below.
Figure 26: ANSYS Model of Prosthetic Shank representing deformation in the body
Additionally, stresses in the body can be calculated.
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Figure 27: ANSYS Model of Prosthetic Shank representing stresses with forces applied in the body
Figure 28: ANSYS Model of Prosthetic Shank including a factor of safety.
Such an analysis can be completed for any segment of a prosthetic leg, either transfemoral or transtibial.
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RESULTS
The following section outlines results from various means for different aspects of the project.
Kinematics
Table 2: Angular Velocities and Accelerations for the Thigh, Shank, and Foot, resolved by the Matlab algorithm in Appendix 3.
Parameter
Angular Velocities Angular Accelerations
Matlab Algorithm
Thigh
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.05 0.1 0.15 0.2
AngularVelocity(rad/s)
Time(s)
-40
-30
-20
-10
0
10
20
30
0 0.05 0.1 0.15 0.2
AngularAcceleration(rad/s^2)
Time(s)
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Table 3: Mass Center Velocities for the Thigh, Shank, and Foot, resolved by the Matlab algorithm in Appendix 3 as well as with SolidWorks
Parameter Computation #1 Compared to #2
Mass Center
Velocities
Matlab Algorithm SolidWorks
Thigh (X)
Thigh (Y)
-0.9
-0.7
-0.5
-0.3
-0.1
0.1
0 0.05 0.1 0.15 0.2
MassCenterVelocity(m/s)
Time(s)
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 0.05 0.1 0.15 0.2
MassCenterVelocity(m/s)
Time(s)
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Table 4: Mass Center Accelerations for the Thigh, Shank, and Foot, resolved by the Matlab algorithm in Appendix 3 as well as with SolidWorks
Parameter Computation #1 Compared to #2
Mass Center
Accelerations
Matlab Algorithm SolidWorks
Thigh (X)
Thigh (Y)
-6
-4
-2
0
2
4
6
0 0.05 0.1 0.15 0.2
MassCenter
Acceleration(m/s^2)
Time(s)
-4
-3
-2
-1
0
1
2
3
4
0 0.05 0.1 0.15 0.2
MassCenterAcceleration
(m/s^2)
Time(s)
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Results Discussion
Some possible reasons for discrepancies between the Matlab outputs, SolidWorks outputs, and Winter et
al. data are outlined below:
Our model takes anatomic geometries into account, whereas the Winter et al. data assumes
cylindrical bodies for the leg segments.
There are differences in how the local and global coordinate systems are defined and utilized
between the SolidWorks computations and those in the Matlab and Winter et al. data.
Our model includes a simplified version of the foot used in the Winter et al. dataset.
The muscular constraints were not included in either our model or the Winter et al. dataset.
The SolidWorks model is 3-dimensional, whereas the Matlab model or the Winter et al. dataset
are both 2-dimensional.
Further analysis would provide better continuity between models and would likely result in more
accurate outputs.
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CONCLUSION
We completed our dynamic analysis of a human leg via both theoretical approach and a more precise and
practical approach from CAD simulation. In the theoretical analysis, Amanda and Jinyi adapted Matlab
code from the midterm project to the new system to perform the forward dynamics, obtained results for
angular velocity, angular acceleration, as well as mass center velocity and acceleration. Furthermore, a
new Matlab program was developed for inverse dynamics focusing on ground reaction force and reaction
force at the knee. Plots of such measurements were generated to have a visual comparison with the CAD
simulation. For the more practical approach, Iman created the CAD model and completed various
simulation to compare with our Matlab simulation results. A 3D model of the human leg was created in
SolidWorks, allowing us to collect the dynamic measurements to compare with the Matlab outputs. We
also compared our inverse dynamic results with the CAD software simulation. We used SIMM, which is a
biomechanics simulation software, for a gait analysis test. We obtain ground reaction force throughout
the gait cycle and center of pressure vs. time. Based off data from SIMM, we were able to conduct a FEA
in ANSYS to examine the reaction forces at the knee. Lastly, we used Quintic Biomechanics’ sample data
for walking gait cycle on the treadmill as a proof of concept for potential future data collection. This could
also be used to measure the gait cycle of an individual with a lower limb prosthetic. This would make
computations for forward and inverse dynamics possible for the prosthetic scenario that we were unable
to accomplish without such data. These motion pictures were also used to prove our data for each
segment’s linear displacement, mass center velocity, as well as mass center acceleration.
We completed our objectives of analyzing the forward and inverse dynamics of a human leg throughout
a gait cycle via Matlab and modelling software simulations. We consolidated our understanding on
forward dynamics and inverse dynamics via Matlab programing, and CAD simulation. We also learned to
use motion capture software, such as Quintic Biomechanics to prove our founding from Matlab and CAD
software.
Throughout the process, the biggest challenge we faced was to perfect the Matlab code for its simulation
to match the real leg motion completed by the CAD software. The Matlab code only performs a perfect
planner motion and neglects joint friction. A human leg’s motion during a gait cycle is actually three-
dimensional and joint friction as well as other noises would change the results from those that we
calculated.
Therefore, to improve our project we need to work on a more precise model for Matlab simulation. To be
more specific, joint friction, muscle effects, and a third dimension of motion needed to be taken into
consideration. In addition, we did not discover any prosthetic gait cycle data. We wished to have such
information to understand the similarities and difference between a human leg and a prosthetic leg, which
would have allowed us to examine functionality discrepancies of an artificial leg, and understand how to
improve its design. For further future studies it might be good to use combination of Quintic Biomechanic
software with SIMM to found the actual forces and moments in each part of segments.
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REFERENCES
1. Amirouche, Farid M. Fundamentals of multibody dynamics:
theory and applications. Boston: Birkhäuser, 2006. Print.
2. de Leva, P., 1996. Adjustments to Zatsiorsky–Seluyanov’s
segment inertia parameters. J. Biomech. 29, 1223–1230.
3. Dumas, Raphael and Cheze, Laurence and Frossard,
Laurent A. (2009) Loading applied on prosthetic knee of
transfemoral amputee: comparison of inverse dynamics
and direct measurements. Gait & Posture, 30(4). pp. 560-
562.
4. L. Ren, R.K. Jones, D. Howard. Whole body inverse
dynamics over a complete gait cycle based only on
measured kinematics. J Biomech, 41 (12) (2008), pp. 2750–
2759
5. S. Chowdhury, N. Kumar. Estimation of Forces and
Moments of Lower Limb Joints from Kinematics Data and
Inertial Properties of the Body by Using Inverse Dynamics
Technique. Journal of Rehabilitation Robotics, pp. 93-98.
6. Winter, David A. Biomechanics and motor control of
human movement. Hoboken, N.J: Wiley, 2009. Print.
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Appendix 3
Matlab Code – Kinematics and Equations of Motion
% Final - Numeric Solution for Forward Dynamics
%
clear all
clc
syms n1 n2 n3 t
g = 9.8;
%% Ask User for Lengths and Masses of Bodies in the System
prompt = {'Lengths of Body 1, 2, and 3 with spaces between (mm)','Masses of Body 1, 2, and 3 with spaces between
(kg)'};
dlg_title = 'System Parameters';
num_lines = 1;
defaultans = {'422.2 434 258.1','10.7894 3.5113 0.9417'};
ans1 = inputdlg(prompt,dlg_title,num_lines,defaultans);
l = str2num(ans1{1,:});
m = str2num(ans1{2,:});
l1 = l(1)/1000;
l2 = l(2)/1000;
l3 = l(3)/1000;
m1 = m(1);
m2 = m(2);
m3 = m(3);
%% Ask User for Time Point of Interest
prompt = {'Provide Time Point of Interest (seconds)'};
dlg_title = 'System Parameters';
num_lines = 1;
defaultans = {'1'};
ans3 = inputdlg(prompt,dlg_title,num_lines,defaultans);
t_sub = str2num(ans3{1,:});
%Choose time point
%user input from other Matlab code
%% Pull angular position, velocity, and acceleration info from Excel file
data = xlsread('Winter_Appendix_data.xlsx','A3.LinearAngularKinematics');
%t_sub = 1.101;
time = data(:,2) == t_sub;
% Initial Angles
th1_o = data(time,23)/57.2958; % Hip Joint (thigh) position at specific time
th2_o = -data(time,13)/57.2958; % Knee Joint (shin) position at specific time
th3_o = data(time,3)/57.2958; % Ankle Joint (foot) position at specific time
% Angular Velocities
th1_dot = data(time,24); % Hip Joint (thigh) velocity at specific time
th2_dot = data(time,14); % Knee Joint (thigh) velocity at specific time
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th3_dot = data(time,4); % Ankle Joint (thigh) velocity at specific time
% Angular Accelerations
th1_dotdot = data(time,25); % Hip Joint (thigh) acceleration at specific time
th2_dotdot = data(time,15); % Knee Joint (thigh) acceleration at specific time
th3_dotdot = data(time,5); % Ankle Joint (thigh) acceleration at specific time
%% Plot the Visual Representation of the Initial Positioning and Size of Robot
system = [0 0;...
sin(th1_o-1.5708)*l1 -cos(th1_o-1.5708)*l1;...
sin(th1_o-1.5708)*l1+sin(th1_o+th2_o-1.5708)*l2 -cos(th1_o-1.5708)*l1-cos(th1_o+th2_o-1.5708)*l2;...
sin(th1_o-1.5708)*l1+sin(th1_o+th2_o-1.5708)*l2+sin(th1_o+th2_o+th3_o-1.5708)*l3 -cos(th1_o-1.5708)*l1-
cos(th1_o+th2_o-1.5708)*l2-cos(th1_o+th2_o+th3_o-1.5708)*l3];
figure (1);
plot(system(:,1),system(:,2),'m-o','LineWidth',2,'MarkerSize',20,'MarkerEdgeColor','c')
title('Position of Leg at Specified Moment in Time');
xlabel('Horizontal Position (meters)');
ylabel('Vertical Position (meters)');
axis([-1*(l1+l2+l3) l1+l2+l3 -1*(l1+l2+l3) 0])
%% Matrix Set-Up
% n-Coordinate Matrix
n = [n1; n2; n3];
% Transformation Matrices and their Time Derivatives
S10 = vpa([cos(th1_dot*t+th1_o) sin(th1_dot*t+th1_o) 0; -sin(th1_dot*t+th1_o) cos(th1_dot*t+th1_o) 0; 0 0 1],3);
S01 = vpa(transpose(S10),3);
S21 = vpa([cos(th2_dot*t+th2_o) sin(th2_dot*t+th2_o) 0; -sin(th2_dot*t+th2_o) cos(th2_dot*t+th2_o) 0; 0 0 1],3);
S20 = vpa(simplify(S21*S10),3);
S02 = vpa(transpose(S20),3);
S32 = vpa([cos(th3_dot*t+th3_o) sin(th3_dot*t+th3_o) 0; -sin(th3_dot*t+th3_o) cos(th3_dot*t+th3_o) 0; 0 0 1],3);
S30 = vpa(simplify(S32*S21*S10),3);
S03 = vpa(transpose(S30),3);
S10_dot = vpa(diff(S10,t),3);
S20_dot = vpa(diff(S20,t),3);
S30_dot = vpa(diff(S30,t),3);
x_dotT = [0 0 th1_dot 0 0 th2_dot 0 0 th3_dot];
x_dotdotT = [0 0 th1_dotdot 0 0 th2_dotdot 0 0 th3_dotdot];
% Identity and Zero Matrices
I = eye(3);
zeroMat = [zeros(3)];
% Partial Angular Velociy Matrices and thier Time Derivatives
omega1 = [I; zeroMat; zeroMat];
omega2 = [I; S10; zeroMat];
omega3 = [I; S10; S20];
omega1_dot = [zeroMat; zeroMat; zeroMat];
omega2_dot = diff(omega2,t);
omega3_dot = diff(omega3,t);
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Appendix 5
Matlab Code – Inverse Dynamics
data = xlsread('dynamics.xlsx','A.forward');
time = data(3:17,2) == t_sub; %counter-clockward is the positive reaction
a_x_ankle = data(time,20);
R_x_ankle= m_3*a_x_foot+R_x; %R_x_ankle is x component of the ankle reaction force
%R_x is the x component of the ground reaction force
a_y_ankle = data(time,21); %R_y_ankle is Y component of the ankle reaction force
R_foot_y= m_3*a_y_foot+m_3*g+R_y; %R_y is the y component of the ground reaction force
M_ankle= M_1 + l_x_ground * R_x+l_y_ground - l_x_ankle * R_x_ankle - l_y_ankle * R_y_ankle
%M_1 is the moment repect to the contact point with the ground
%l_x_ground is x component of the moment arm respect ground contact point
%l_y_ground is the y component of moment arm respect to ground contact point
%l_x_ankle is x component of the moment arm respect to ankle
%l_y_ankle is the y component of moment arm respect to ankle
a_x_shin = data(time,13);
a_y_shin = data(time,14);
R_x_shin= m_2*a_x_shin+R_x_ankle; %R_x_shin is x component of the shin reaction force
R_y_shin= m_2*a_y_shin+m_2*g+R_y_ankle; %R_y_shin is x component of the shin reaction force
M_shin= M_ankle + l_x_ankle * R_x + l_y_ankle - l_x_shin * R_x_shin - l_y_shin * R_y_shin
%l_x_shin is x component of the moment arm respect to ankle
%l_y_shin is the y component of moment arm respect to ankle
R_Knee= M_shin * l_knee
%R_knee is the reaction force at the knee
%l_knee is the moment arm respect to the center of pressure of the shin