Forward Kinematics Modelling Using Modified Fuzzy Inference

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Ankle Complex

Human ankle joint is a very complex bony structure in the human skeleton [143] and is fundamentally a combination of two joints (Figure 3.1). The first joint is called the ankle joint which is made up of three bones: the lower end of the tibia (shinbone), the fibula (the small bone of the lower leg) and the talus (the bone that fits into the socket formed by the tibia and the fibula). The talus sits on top of the calcaneus (the heel bone) and moves mainly in one direction. The ankle joint works like a hinge, to allow up, (dorsiflexion) and down (plantar flexion) foot motions. The second joint is the subtalar joint, also known as the talocalcaneal  joint which is a joint of the foot. It occurs at the meeting point of the talus and the calcaneus.
This joint is responsible for the inversion and eversion of the foot, but plays no role in dorsiflexion or plantarflexion motion. However it is very much a part of the ankle joint and thus is important. Figure 3.1: (a) The Ankle joint anatomy and (b) ankle motion trajectories for right foot (±θ inversion and eversion, ±ψ plantarflexion and dorsiflexion, ±φ abduction and adduction).
There is one more joint (normally not considered as part of the ankle joint) called MTP (metatarsophalangeal) joint connecting fore and the rear with Calcaneus, Cuboid and Navicular bones as shown in Figure 3.1a. The raising and lowering motions of the toes and the heel are achieved about this joint. In the present study the ankle and the subtalar joints have been collectively considered as one joint providing three rotational degrees of freedom and are called ankle joint henceforth for simplicity. Since this study is limited to the ankle joint motions and not the fore foot motions, the MTP joint and related motions are not considered. The ankle joint can have rotations in all three planes namely, sagittal, frontal and transverse planes. The sagittal plane is contained by the x and the z-axes and ankle movements in this plane occur about the y-axis (Figure 3.1b). Ankle motions in the sagittal plane are termed as plantarflexion and dorsiflexion as shown in Figure 3.2. The transverse plane is defined by the x and y axes and movements in this plane occur about the z-axis. Motions in the transverse plane are defined as adduction (when the right foot toes are moved towards the left foot) and abduction (when the right foot toes are moved away from the left foot). The frontal plane is formed by the y and the z-axes and the ankle motions in this plane occur about the x-axis. Frontal plane motions of the ankle joint are termed as inversion (when the inner side of the foot also known as medial side is lifted up) and eversion (when the inner side of the foot is pushed down) (Figure 3.2). Various ankle movements suggested by Siegler

Ankle Injuries and Physiotherapy

Ankle injuries [143] are one of the most common injuries in sports and daily life. For example, youngsters are subjected to ankle injuries from sports and whilst carrying excessive load, and children and the elderly are injured from walking on uneven surfaces and bone weakness. Non-functionality of ankle joint is also quite common for stroke surviving patients. Common ankle injuries are sprain, strain and fracture. An overstretched muscle or tendon can often cause strain which is a mild injury. However if a ligament is overstretched it causes more serious injury called sprain which results in pain and joint non-functionality. Sometimes when a ligament is overstretched and broken it may pull off a piece of bone causing a fracture [148].
Ankle joint is predominately subjected to the sprain injuries resulting from overstretched ligaments. International studies report that [149] ankle sprains contribute to 15-20% of all sports related injuries. Referring to the study conducted by the Effective Practice Institute, University of Auckland, ankle sprains cause a significant cost to ACC (Accident Compensation Corporation), New Zealand [149]. In the year 2000/01, apart from the 17,200 ongoing claims, 82,000 new claims, amounting over $19 million were received by ACC. Expenses on part of new and ongoing ankle claims, ranked fourth largest cost to ACC after the lower back, neck and shoulder injuries. During a study conducted in the United States for epidemiology of ankle sprain, it was found that 2.15 incidents of ankle sprain per 1000 persons, were recorded during 2002-2006 [150].
Primary treatment for ankle injuries [5] includes, rest, ice, compression and elevation (RICE) of the affected foot-ankle entity. Application of ice after rest is used to reduce swelling, compression stockings are used to firmly support the foot-ankle body and elevation helps to minimize further swelling. The primary treatment should be followed by stretching and motion therapy along with partial weight bearing to maintain mobility in the ankle joint. Motion therapy is recommended to start within 72 hrs of the injury, to prevent muscular atrophy which may lead to a reduced range of motion (ROM). Motion therapy also stimulates healing of the impaired ligaments [151]. Once the ROM is achieved, strengthening of weakened muscles is essential for rapid recovery and is a preventive measure against further injury. As patients achieve full weight bearing capability without pain, proprioceptive exercise is initiated for the recovery of balance and postural control using wobble boards.
Finally, advanced exercises using uneven surface wobble board should be performed to regain functions specific to normal activities. The ankle joint is an important joint in human skeleton since it is responsible to carry the body weight and maintain balance during gait. It is subjected to high impact forces which may be as high as several times of the body weight (e.g. while jumping). It is a very strong joint with stiffer muscles and hence offers large moments as shown in Table 3.1. In light of the above facts, it can be concluded that apart from the ROM capabilities, wearable robotic device for ankle rehabilitation should have higher payload capacity to provide required passive and resistive moments at the ankle joint.

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Chapter 1 Introduction
1.1 Rehabilitation and Robots
1.2 Wearable Robots for Rehabilitation .
1.3 Research Objectives
1.4 Thesis Delineation
1.5 Chapter Summary
Chapter 2 Literature Review 
2.1 Wearable Robots
2.2 Contemporary Ankle Rehabilitation robots
2.3 Forward Kinematics of Parallel Robots
2.4 Parallel Robot Design Analysis.
2.5 Multi-objective Optimization
2.6 System Modelling and Control of PMA
2.7 Discussion
2.8 Chapter Summary
Chapter 3 Wearable Ankle Robot: Development and System Modelling 
3.1 Human Ankle, Potential Disorders and Physiotherapy .
3.2 Design Specifications
3.3 Conceptual Design and Construction
3.4 Symbolic Kinematic Modelling
3.5 Geometric Modelling
3.6 Dynamic Modelling
3.7 Chapter Summary
Chapter 4 Forward Kinematics Modelling Using Modified Fuzzy Inference
4.1 Forward Kinematics
4.2 Forward Kinematics Solutions
4.3 Fuzzy Inference Approach
4.4 Optimization of Fuzzy Inference System
4.5 Training Data and Results
4.6 Discussion
4.7 Chapter Summary .
Chapter 5 Design Analysis of the Wearable Ankle Robot 
5.1 Kinematic Design
5.2 Actuation Design
5.4 Chapter Summary
Chapter 6 Single Objective Design Optimization of the Wearable Ankle Robot
6.1 Robot Geometrical Parameters .
6.2 Optimization of Global Condition Number (GCN)
6.3 Results and Discussion
6.4 Chapter Summary
Chapter 7 Multi-objective Design Optimization of the Wearable Ankle Robot 
Chapter 8 Pneumatic Muscle Actuator Modelling and Fuzzy Logic Control 
Chapter 9 Conclusions

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Design Analysis and Control of Wearable Ankle Rehabilitation Robot

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