Theory of Force Adaptation

Dynamic balance has been studied to eliminate the shaking forces and vibration at the base induced by rapid motion of robotic devices. This is done by designing the mass distribution such that the total center of mass of the mechanism is stationary for all motions. However, when the payload changes, for example during pick-and-place action, the dynamic balance cannot be maintained, and vibrations will appear, reducing the accuracy. In this paper, five strategies are described to adapt the dynamic balance under varying payload conditions. Three of these strategies rely on reconfiguration of the mechanism; by changing position the counter weights (I), by changing the joint locations (II) or by altering the amount of counter weight (III). The last two strategies use active control of additional linkages to steer the mechanism in over a reactionless trajectory. These additional linkages can be placed at the base as a reaction mechanism (IV), or within the kinematic chain with redundant joints (V). The implications and differences of these strategies are shown by applying them to a 3 degree of freedom (DOF) planar mechanism. All strategies can provide adaptive dynamic force balance, but have different features, especially added complexity (II & III), reconfiguration force (I & III), or energy consumption (IV & V)

Bidirectional Human-Robot Learning: Imitation and Skill Improvement

Recently creation continuously variable transmission (CVT) having property of the adaptation to variable technological loading develops. Traditional CVT contains the hydraulic converter and gear differential with two degrees of freedom (patents of Crockett, Volkov). The hydraulic converter imposes differential constraint on movement of links of the mechanism with two degrees of freedom. It provides definability of movement of transmission. Take place progressive CVT without use of the hydraulic converter (Harries’s patent, Ivanov’s patent). Such transmission contains only gear differential with two degrees of freedom. However the theoretical substantiation of serviceability of such transmission is not convincing for the lack of the proof of static definability of the mechanism with two degrees of freedom, having only one input. Ivanov K.S.’s theoretical researches do not contain enough convincing arguments of presence of definability of such mechanisms. Mechanisms with two degrees of freedom are considered disabled because of their contradiction to a key rule of mechanics that the number of the generalized coordinates should be equal to number of degrees of freedom of the mechanism (that is it should be equal to two, instead of to one). In Ivanov K.S.’s early works it was mentioned presence of paradox of the mechanics reflecting essence of the specified discrepancy. However in these works there was no the elementary demonstrative base of essence of the phenomenon resulting in static definability. The purpose of the present work to describe essence of the phenomenon which in certain conditions result to static definability of the mechanism with two degrees of freedom at presence only of one input, to receive the theoretical description of paradox of mechanics and its authorization using the elementary laws of theoretical mechanics. In the work the presence of paradox of mechanics is proved. The paradox of mechanics takes place in the kinematic chain having the closed contour, and it consist in the following. The structural group with two degrees of freedom having two consistently connected links is statically definable at presence only one entrance link. The paradox of mechanics is authorized by the account of additional constraint which is imposed by kinematic chain with the closed contour and two degrees of freedom on movement of links by a principle of possible works. Use of the equations of a statics and additional constraint allows to receive the equations of interrelation of parameters of transmission and to execute synthesis of transmission on the set conditions of motion. The found laws will allow creating the transfer mechanisms having property of mechanical adaptation to variable technological loading. Mechanical adaptation provides an opportunity of motion of an output link with a speed inversely force of resistance at constant input power.

Despite several clinical tests that have been developed to qualitatively describe complex motor tasks by functional testing, these methods often depend on clinicians' interpretation, experience and training, which make the assessment results inconsistent, without the precision required to objectively assess the effect of the rehabilitative intervention. A more detailed characterization is required to fully capture the various aspects of motor control and performance during complex movements of lower and upper limbs. The need for cost-effective and clinically applicable instrumented tests would enable quantitative assessment of performance on a subject-specific basis, overcoming the limitations due to the lack of objectiveness related to individual judgment, and possibly disclosing subtle alterations that are not clearly visible to the observer. Postural motion measurements at additional locations, such as lower and upper limbs and trunk, may be necessary in order to obtain information about the inter-segmental coordination during different functional tests involved in clinical practice. With these considerations in mind, this Thesis aims: i) to suggest a novel quantitative assessment tool for the kinematics and dynamics evaluation of a multi-link kinematic chain during several functional motor tasks (i.e. squat, sit-to-stand, postural sway), using one single-axis accelerometer per segment, ii) to present a novel quantitative technique for the upper limb joint kinematics estimation, considering a 3-link kinematic chain during the Fugl-Meyer Motor Assessment and using one inertial measurement unit per segment. The suggested methods could have several positive feedbacks from clinical practice. The use of objective biomechanical measurements, provided by inertial sensor-based technique, may help clinicians to: i) objectively track changes in motor ability, ii) provide timely feedback about the effectiveness of administered rehabilitation interventions, iii) enable intervention strategies to be modified or changed if found to be ineffective, and iv) speed up the experimental sessions when several subjects are asked to perform different functional tests.

The analysis of the biomechanics of the leg while cycling is based on assumptions that make the calculations easier or faster. Most of the models and optimisations based on the dynamic chains introduced by Gonzalez & Hull (Hull & Gonzalez, 1988: J. Biomechanics, 21(10), 839-849) and by Papadopoulos (Papadopoulos, 1987: Biomechanics in Sport, 6, 83-92) with 5 and 4 links respectively share many of these assumptions. For instance, a fixed or no distance from the seat to the centre of rotation of the hip, a constant length of the segments of the leg (thigh, shank and foot) or a constant angular speed of the crank. Previous work (Rios Soltero et al., 2014: Procedia Engineering, in press) has shown that these assumptions may have an influence on the inertial forces of the system. The present study shows that the generalised forces at the knee and ankle would also be different. As it was done before (Rios Soltero et al, 2014), the dynamic chain consisted of three leg segments (thigh, shank and foot), a crank and a grounding element. Also, three motion models were used to calculate the forces at each instant of the pedalling cycle in the sagittal plane at the knee and ankle (Figure 1.a). Here, the analysis was based on the force data at the pedal reported by Boyd et al. (1996, J. Biomechanics, 29(8), 1105-1110), and the motion capture of markers located at the leg and pedal from Rios Soltero et al. (2014). The crank speed was calculated from the pedal marker. To get the orientation angle of each segment, the first two models used a linear regression of their markers. One of them (Inters; intersections method) intersected each line of contiguous segments (thigh with shank and seat-tube, shank with foot and thigh, foot with crank and shank, and crank with seat-tube and foot) to create a dynamic chain at each instant. This allowed a change in length of the segments and the motion of the hip. The second method (Proj; projections method) only uses the orientation of the linear regression for each segment, while their lengths were constant as measured directly from the person. In this way, neither the hip nor the length of the segments were fixed. The third method (Kin; kinematics method) reproduced the assumptions of other studies: a hip fixed at the seat and unvarying length of the leg segments. The length of the leg segments was calculated according to anatomical tables (Winter, 2004: Biomechanics and motor control of human movement (3d ed.). John Wiley & Sons). To calculate the position of the thigh at each instant, an 8th-degree polynomial regression was calculated between the angle of the crank and that of the thigh. In all cases, the centre of mass and mass-moment of inertia of the thigh and shank were calculated using an analytical equation based on the geometry proposed by Durkin Teague et al. (2005: J. Biomechanical Engineering 127, 455-464) and Durkin and Dowling (2006: Annals of Biomedical Engineering 34, pp. 1483-1493). An elliptical frustum was used for the foot. The results of the analysis show a slight difference in the moments at the ankle and the knee for the first half of the cycle (Figure 1.b). The maximum absolute difference in the case of the knee is 15.4 N·m (between Inters and Kin) which is around 13% of the values' range. As for the ankle, it is 7.79 N·m (between Inters and Proj) with a 19% of the values' range. It is clear that there is no qualitative difference between the models. However, further analysis is needed to determine if there is a significant effect.

Abstract. The similarity recognition of kinematic chains (KCs) is helpful for improving the efficiency of configuration synthesis, which has been paid more and more attention in recent years. The existing recognition methods are divided into the definition method and feature constant method. Among them, the definition method is difficult to adopt in practice because of its long operation time, especially when the number of similar vertices in KCs is large. In this paper, the new concepts of a loop tree (LT) and a loop tree matrix (LTM) have been proposed, which improve the efficiency of similarity recognition. This method is applied on the complete structure of the following: 8-link with 1 DOF (degree of freedom), 9-link with 2 DOF, 10-link with 1 DOF, 12-link with 1 DOF, 13-link with 2 DOF, 14-link with 3 DOF, 15-link with 4 DOF planar single-joint KCs, and contracted graphs with up to six independent loops. All results are verified by the definition method to prove the good applicability, reliability, and efficiency of the proposed method. Simultaneously, the application case of the similarity recognition in a mechanism creation is given to provide a reference for an innovative design.

There is no dearth of methods to test isomorphism amongst kinematic chains. Search for a computationally easier, logically simple and unique method is still on. Present work is in quest of a reliable test to detect isomorphism among kinematic chains. Work presented here is more versatile as it incorporates more features of the kinematic chain which were not included earlier such as number and type of links, their relative dispositions in the kinematic chain, nature of adjacent links etc. The method proposed is based on the concept of pseudo-probability (pseudo means it appears to be, but not exactly. The approach does not follow in-toto the principles of probability and considerable liberty has been taken in interpreting the word probability hence the word pseudo is used along with the probability schemes). Using the resemblance of different coloured balls in an urn for the number and type of links in a kinematic chain, a matrix (named P-Matrix) representing the kinematic chain in totality is generated. For the sake of comparison a numerical scheme named, pseudo probability scheme, P-Scheme, is developed from the above P-Matrix and is used for testing isomorphism. In fact the method is more powerful in the sense that each row of the proposed P-Matrix is capable of representing the respective kinematic chain distinctly and can be used to compare the kinematic chains with same link assortments, uniquely. The proposed method, besides possessing the potential of testing the isomorphism among simple-joint, single degree of freedom kinematic chains is also capable of multi degrees of freedom and multiple-joint kinematic chains.

Building pounding philosophy is the collision of adjacent buildings when earthquake take place and buildings show lateral movement. Providing suitable separation distance, impact force precludes and reduces the failure of construction elements. In this paper, building pounding between two reinforced concrete buildings with insufficient gap size is numerically investigated in order to study the impact force during seismic excitations. For this challenge, two to three story concrete buildings are modeled by finite element software. On the other hand, two mathematic models of RC buildings with lumped masses are considered to get the results of pounding and effect of impact on structural behavior. A mathematic program is used based on single degree-of-freedom (SDOF) equations to analyze the failure of models. Since calculation of impact forces depends significantly on link element assigned between two bodies, special link element is utilized. Used link element between two buildings is included in a spring with high stiffness and a viscous impact dashpot, which were located parallel in order to absorb the energy loss during impact. Finally, a new equation of motion is suggested to calculate the impact force. The accuracy of suggested equation is confirmed by energy equation. Key words: Building pounding, impact, dissipated energy, finite element.

Effects of seat height on muscular pattern and interlimb coordination in cycling

An efficient parallel algorithm for forward dynamics computation of human figures is proposed. The algorithm is capable of handling any kinematic chains including structure-varying ones. The asymptotic complexity of the algorithm is O(N) in serial computation and O(log N) in parallel computation on O(N) processors for most practical kinematic chains. The idea is to assemble a kinematic chain by adding the joints one by one and compute the constraint forces at the new joints using the principle of virtual work. The parallelism of the algorithm can be adapted for parallel processing systems with any number of processors by simply changing the assembly order. Simulation examples on an 8-node cluster demonstrate the effectiveness of the algorithm.

Parallel-structure mechanisms with four degrees of freedom and four kinematic chains are discussed. The synthesis of these manipulators were performed using a device of closed screw groups. This approach allows avoiding complex equations of synthesis and analysis of singularities. Kinematic chains may impose equal constraints or different constraints, and each may contain a drive. The main result of this article is the synthesis of a new parallel-structure mechanism and a screw analysis of constraints imposed by the kinematic chains.

For a spherical in-parallel actuated mechanism with three degrees of freedom in which the output link is connected to the base link by three connecting chains composed of an input link, a coupler link and three revolute pairs each, a transmission index (TI) is proposed based on the power transmitted from the input links to the output link. Static force analyses with consideration of elasticity of links have been carried out in the case where forces and moments are exerted on the output link as external loads. Then, mechanism synthesis is carried out considering both motion transmissibility and interferences among links, and a spherical in-parallel actuated mechanism with three degrees of freedom is proposed.

For a spherical in-parallel actuated mechanism with three degrees of freedom in which the output link is connected to the base link by three connecting-chains composed of an input link, a coupler link and three revolute pairs each and moments are transmitted only in a specific direction from each coupler link to the output link, transmission index (TI) is proposed based on the power transmitted from input links to the output link. Static force analyses with consideration of elasticity of links have been carried out in the case where forces and moments are exerted on the output link as external loads, and a new mechanism design method of a spherical in-parallel actuated mechanism using transmission index which can be calculated only from geometrical conditions of the mechanism is derived. A spherical in-parallel actuated mechanism with three degrees of freedom with large working space, in which motion transmissibility is excellent and interferences among links do not occur, is proposed.

The paper presents a modified Denavit-Hartenberg coordinate system resulted from joint application of graph theory and the Denavit-Hartenberg coordinate system, which was developed to describe the kinematics of robot actuators with a linear open kinematic chain. It allows forming mathematical models of actuating mechanisms for the robots with tree-like kinematic structures. The work introduces the concept of primary and auxiliary coordinate systems. It considers an example of making the links’ reachability matrix and reachability graph for the tree-like actuating mechanism of a robotic mannequin. The use efficiency of the proposed modified Denavit-Hartenberg coordinate system is illustrated by the examples giving the mathematical description of the kinematics and dynamics of specific robots’ tree-like actuating mechanisms discussed in the previously published papers. It is shown that the proposed coordinate system can also be successfully applied to describe the actuating mechanisms of robots with a linear open kinematic chain, which is a particular case of the tree-like kinematic structure. The absence of branching joints in it does not require introducing auxiliary coordinate systems and the parameters f(i) and ns(i) are necessary only for the formal notation of equations, which have similar forms for the tree-like and linear chains. In this case, the modified and traditional coordinate systems coincide.

Field observations have been repeatedly reported on the galloping of transmission lines having only a small acretion of ice of the order of 10% of the diameter on the windward side. Aerodynamic force measurements in wind tunnels reveal that significant lift forces are present, having a steep gradient with respect to angle of attack, and which satisfy the Den Hartog negative damping criteria. Drag forces are essentially constant, and aerodynamic moments are zero over the 3600 range of angle of attack. Similarly, no unbalanced inertia forces exist for such light-ice deposits, which precludes the dynamic inertia coupling between galloping and torsion modes. Blow back of the conductor is shown to explain such galloping owing to the angle of attack reaching the critical range, Within a finite range of wind speed. The addition of control devices, identified as the windamper, and the detuner, is shown to modify the distribution of angle of attack along the span, thus altering the angle of attack ‘exposure’ compared with that of an untreated span. Stability analyses in two degrees of freedom (galloping and dynamic twist) are performed for a number of representative cases. Stability is expressed as the root locus of a fourth-degree polynomial (quartic) equation, as a function of wind speed. Perforated cylinder dampers are also considered, and they are found to supply inadequate damping for control, unless the span coverage is unreasonably large. The twisting effect of the Windamper is shown to be its primary stabilising influence. The detuner appears to increase the range of instability in two out of three cases.