The gravity balancing exoskeleton, designed at University of Delaware, Newark, consists of rigid links, joints and springs, which are adjustable to the geometry and inertia of the leg of a human subject wearing it. This passive exoskeleton does not use any motors but is designed to unload the human leg joints from the gravity load over its range-of-motion. The underlying principle of gravity balancing is to make the potential energy of the combined leg-machine system invariant with configuration of the leg. Additionally, parameters of the exoskeleton can be changed to achieve a prescribed level of gravity assistance, from 0% to 100%. The goal of the results reported in this paper is to provide preliminary quantitative assessment of the changes in kinematics and kinetics of the walking gait when a human subject wears such an exoskeleton. The data on kinematics and kinetics were collected on four healthy and three stroke patients who wore this exoskeleton. These data were computed from the joint encoders and interface torque sensors mounted on the exoskeleton. This exoskeleton was also recently used for a six-week training of a chronic stroke patient, where the gravity assistance was progressively reduced from 100% to 0%. The results show a significant improvement in gait of the stroke patient in terms of range-of-motion of the hip and knee, weight bearing on the hemiparetic leg, and speed of walking. Currently, training studies are underway to assess the long-term effects of such a device on gait rehabilitation of hemiparetic stroke patients.

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This paper outlines the design of a wearable upper arm exoskeleton that can be potentially used to assist and train arm movements of stroke survivors or subjects with weak musculature. In the last 10 years, a number of upper arm training devices have emerged. However, due to their size and weight, their use is restricted to clinics and research laboratories. Our proposed wearable exoskeleton builds upon our research experience in wire driven manipulators and design of rehabilitative systems. The exoskeleton consists of three main parts: (i) an inverted U-shaped cuff that rests on the shoulder, (ii) a cuff on the upper arm, and (iii) a cuff on the forearm. Six motors mounted on the shoulder cuff drive the cuffs on the upper arm and forearm with the use of cables. In order to assess the performance of this exoskeleton prior to use on humans, a laboratory test-bed has been developed where this exoskeleton is mounted on a model skeleton, instrumented with sensors to measure joint angles. This paper describes the design details of the exoskeleton and addresses the key issue of parameter optimization to achieve a useful workspace based on kinematic and kinetic models. The optimization results have also been motivated from activities of daily living.

where 2 m ; Q 2 m2m is non-Hurwitz; (1) 2 m is a causal forcing term described by the unknown LTI system of differential (12).The vector g(t) 2 m is constrained bŷ (k) + p k01 (k01) + 1 1 1 + p 1 _ + p 0 = F k01 g(t) (k01) + 1 1 1 + F1 _ g(t) + F0g(t) (36) where the numbers p0; p1; . . . ; p k01 are the coefficients of the characteristic polynomial (17), and the matrices F k01 ; . . . ; F 1 ; F 0 2 m2mare to be selected. One can uncouple (35) and (36) where the coefficients C 0 ; C 1 ; . . . ; C k01 are selected to provide any desired convergence rate of g(t) ! 0.Matrices F k01 ; . . . ; F1;F0 2 m2m are calculated by equating similar terms on the left and right hand sides of (39) as. . .from whereSubstituting (40) and (41) into (38) we obtain (19) and (20). As soon as the term g(t) converges to zero, the two linear differential equations _ = Q + (1) + g(t); and _ = Q + (1)will have an identical structures and the same forcing term (1) which proves the convergence ! as claimed. The theorem is proven. Int. J. Syst. Sci., vol. 38, no. 11, pp. 871-878, 2007. [11] A. Levant, "Higher order sliding modes, differentiation and output feedback control," Int. J. Control, vol. 26, no. 9, pp. 924-942, 2003. REFERENCES Differential Flatness of a Class of -DOF Planar Manipulators Driven by 1 or 2 ActuatorsJaume Franch, Sunil K. Agrawal, and Vivek Sangwan Abstract-A fully actuated system can execute any joint trajectory. However, if a system is under-actuated, not all joint trajectories are attainable. In recent years, the authors have actively pursued novel designs of underactuated robotic arms which are both controllable and feedback linearizable. These robots can perform point-to-point motions in the state space, but potentially can be designed to work with fewer actuators, hence with lower cost. With this same spirit, the technical note investigates the property of differential flatness for a class of planar under-actuated open-chain robots having a specific inertia distribution, but driven by only one or two actuators. This technical note addresses the following theoretical question: What placement of one or two actuators will make an n-DOF planar robot differentially flat if it is designed so that its center of mass always lies at joint 2? Index Terms-Differential flatness, robot design, under-actuated robots.

Under-actuated systems are unavoidable in certain applications. For example, a biped can not have an actuator between the foot and the ground. For industrial robots, underactuation is preferable due to cost considerations. A fully actuated system can execute any joint trajectory. However, if the system is under-actuated, not all joint trajectories are attainable. For such systems, it is difficult to characterize attainable joint trajectories analytically and numerical methods are generally used to characterize them. This paper investigates the property of differential flatness for under-actuated planar open chain robots and study its dependence on inertia distribution within the system. Once this property is established, trajectory between any two points in its differentially flat output space is feasible and can be shown to be consistent with the dynamics of the under-actuated system. It is shown that certain choices of inertia distributions make an under-actuated open-chain planar robot with revolute joints feedback linearizable, i.e., also differentially flat. Hence, both cyclic and point to point trajectories can be guaranteed with these under-actuated systems. The methodology proposed is demonstrated with an under-actuated three degree-of-freedom planar robot.