Kinematic Chain Research Articles

On efficient computation of rational {1,2}-pseudo-inverses for multivariable rational matrix-valued functions and their applications

In this article we consider the problem of the existence of rational 1,2-pseudo-inverses for rational multivariable matrix-valued functions. We prove that any rational multivariable matrix-valued function has rational 1,2-pseudo-inverse and we describe the set of all 1,2-pseudo-inverses of a given function, in terms of rational free parameters. It is shown that the 1,2-pseudo-inverse can have an effective description relative to the Moore–Penrose pseudo-inverse (that in general is not even rational), thus making it an alternative effective solution to the problem of online matrix inversion of large matrices that depend on real-time measured parameters. The rationality of the 1,2-pseudo-inverse is crucial when it should be realized in the physical real world (e.g. in inverse control), in contrast with realizations in computer algorithms (e.g. in image processing and communication systems) where the rationality is not necessary but the effective description of the pseudo-inverse becomes crucial. The results has applications in control systems, robust control, inverse control, mechanical systems, kinematic chains, kinematic networks, multi-degree-of-freedom systems, image processing, signal processing and communication systems.

The Kinematics of a Bipod R2RR Coupling between Two Non-Coplanar Shafts

The paper presents a new solution for motion transmission between two shafts with non-intersecting axes. The structural considerations fundament the existence in the structure of the mechanism of three revolute pairs and a bipod contact. Compared to classical solutions, where linkages with cylindrical pairs are used, our solution proposes a kinematical chain also containing higher pairs. Due to the presence of a higher pair, the transmission is much simpler, the number of elements decreases, and as a consequence, the kinematical study is straightforward. Regardless, the classical analysis of linkages cannot be applied because of the presence of the higher pair. For the proposed spatial coupling, the transmission ratio is expressed as a function of constructive parameters. The positional analysis of the mechanism cannot be performed using the Hartenberg–Denavit method due to the presence of a bipod contact, and instead, the geometrical conditions of existence for the bipod contact are applied. The Hartenberg–Denavit method requires the replacement of the bipodic coupling with a kinematic linkage with cylindrical (revolute and prismatic) pairs, resulting in complicated analytical calculus. To avoid this aspect, the geometrical conditions required by the bipod coupling were expressed in vector form, and thus, the calculus is significantly reduced. The kinematical solution for the proposed transmission can be obtained in two ways: first, by considering the equivalent transmission containing only cylindrical pairs and applying the classical analysis methods; second, by directly expressing the condition of definition for the higher pairs (bipodic pair) in vector form. The last method arrives at a simpler solution for which analytical relations for the positional parameters are obtained, with one exception where numerical calculus is needed (but the precision of this parameter is controlled). The analytical kinematics results show two possibilities of building the actual mechanism with the same constructive parameters. The rotation motions from the revolute pairs, internal and driven, and the motions from the bipod joint were obtained through numerical methods since the equations are very intricate and cannot be solved analytically. The excellent agreement validates the theoretical solutions obtained and the possibility of applying such mechanisms in technical applications. The constructive solution exemplified here is simple and robust.

Influence of Contact Surfaces’ Impact on the Gear Profile during Hobbing Process

This work is the result of research on the dynamic process that occurs during milling machining, namely, the influence of the contact surfaces’ impact on the gear and the hob and the influence of their displacements on the resulting profile of the tooth. An acquisition system was placed on the final elements of the milling machine chain to determine the torque moments and displacements during gear milling. The experimental analysis proves that the displacements are within admissible limits and have no major influence on the quality of the processing surfaces. A dynamic simulation of the hobbing process with the finite element method (ANSYS) was performed for a limited period of time, and the values of deformation, equivalent strain, and stress have been determined; the time at which the chips come off and the corresponding value of the equivalent stress that occurs at their break were determined based on the maximum distortion energy von Misses theory. It is required to simulate the entire hobbing process, even if it can be time-consuming to differentiate the influence of the dynamic behavior of the machine’s kinematic supplementary chains on the hob wear and the tooth profile. A modal analysis will be able to support the comparative study related to the obtained experimental data.

Physiotherapy Management in Meniscus Injury

Background: Meniscus injury is one of the most common knee injuries in the orthopedic field. This injury often occurs in sports that involve rotating movements, squats/excessive knee joint flexion such as in basketball, soccer or badminton. The medial meniscus is injured more often than the lateral meniscus, and this is due to the tight attachment of the meniscus to the medial collateral ligament of the knee joint, which limits its movement. Injury occurs when the femur rotates about the tibia, or the tibia against the femur, with the knee joint slightly flexed and supporting body weight. Objective: This study aims to summarize secondary data related to meniscus injuries. Methods: The research method used was a literature study using secondary data in the form of journals related to the topic of meniscus injury obtained through Google Scholar, Science Direct, and PubMed. Results: Several studies have shown that someone with a knee injury can be given physiotherapy intervention in the form of exercise that is tailored to the symptoms experienced. Conclusion: Based on the results of a literature review, neuromuscular and strengthening exercises, Mulligan's squeeze technique with conventional therapy, open and closed kinematic chain and education can improve symptoms after meniscus injury.

Calibration of industrial robots with spherical joint using single wire encoder

Demands for affordable robot calibration are increasing recently due to collaborative robots and virtual manufacturing. This study proposes a method using a single wire encoder as an affordable device. Unlike previous studies focused on compensating errors from wire sagging and fixture itself, this method utilizes the alignment between spherical joint and wire end by finding minimum wire length. After the optimal joint angles #4 and #5 are found by grid search and polynomial least-square regression, closed-loop kinematic chain and linear least square are utilized to find calibration parameters. With 576 datasets, the position error was reduced from 2.43 mm to 0.78 mm.

Bioinspired flapping wing UAV and its kinematic analysis—a novel approach

A rich development in the domain of flapping wing Unmanned Aerial Vehicle (FWUAV) is not yet entirely sufficient to implement the findings of real-life situations. Using the limited knowledge of this domain, this work enlightens the scientific community by introducing a homegrown, patented flapping mechanism of foldable wing aerial vehicle. The synchronized dual wing flapping mechanism consists of a crank slotted lever, a gear train and a special type of 4 bar kinematic chain. The entire sets are powered by a DC motor through crank connected motor shaft. Flapping cycle works on quick return principle generated by crank slotted lever mechanism and foldable wing structure by the special type 4 bar chain with gear train ensure the controlled flapping frequency, twist angle, altitude gain and attitude parameters (Pitch, roll, yaw). This work majorly focuses on the kinematics of the developed bio mimic mechanism by observing the variation of flapping wing orientation, angular velocity and angular acceleration with respect to the crank rotation as well as different crank speeds. These analytically obtained kinematic parameters are further validated after developing a three-dimensional model of the said mechanism as well as multibody analysis by MSC ADAMS. The patterns of the kinematic parameters such that angular displacement, angular velocity and angular acceleration between output and input links are similar and its validation guarantees the correctness of developed mechanism. The kinematic analyzes of linkages are also essential for dynamic study as well as fabrication of prototype.

Analytical Modeling of a New Compliant Microsystem for Atherectomy Operations.

This work offers a new alternative tool for atherectomy operations, with the purpose of minimizing the risks for the patients and maximizing the number of clinical cases for which the system can be used, thanks to the possibility of scaling its size down to lumen reduced to a few tenths of mm. The development of this microsystem has presented a certain theoretical work during the kinematic synthesis and the design stages. In the first stage a new multi-loop mechanism with a Stephenson’s kinematic chain (KC) was found and then adopted as the so-called pseudo-rigid body mechanism (PRBM). Analytical modeling was necessary to verify the synthesis requirements. In the second stage, the joint replacement method was applied to the PRBM to obtain a corresponding and equivalent compliant mechanism with lumped compliance. The latter presents two loops and six elastic joints and so the evaluation of the microsystem mechanical advantage (MA) had to be calculated by taking into account the accumulation of elastic energy in the elastic joints. Hence, a new closed form expression of the microsystem MA was found with a method that presents some new aspects in the approach. The results obtained with Finite Element Analysis (FEA) were compared to those obtained with the analytical model. Finally, it is worth noting that a microsystem prototype can be fabricated by using MEMS Technology classical methods, while the microsystem packaging could be a further development for the present investigation.

A novel hybrid machine tool integrating a symmetrical redundantly actuated parallel mechanism: Design, kinematics, prototype and experiment

Hybrid machine tools are suitable for machining structural components with complex geometries due to their merits of flexible posture adjustment and quick dynamic response. This paper proposes a novel hybrid machine tool with 5-axis machining capability by integrating a newly invented redundantly actuated parallel mechanism (RAPM). For this purpose, a screw theory based type synthesis methodology is proposed to synthesize a RAPM with a topology of 2PRU-(2PRU)R. The synthesized RAPM is conceptually designed as a spindle head, which is characterized by symmetrical limb arrangement and usage of only PRU-type kinematic chains. The spindle head is further integrated with a two-sliding gantry to construct a novel 5-axis hybrid machine tool. The kinematic performances of position and singularity of the proposed hybrid machine tool are analyzed. After then, a laboratory prototype of the hybrid machine tool is engineered and an open-architecture numerical control system is developed to perform 5-axis machining tasks. The large orientation capacity and 5-axis machining capability of the hybrid machine tool are verified by some motion experiments and machining tests.

EXPERIMENTAL RESEARCH THE MECHANISMS WITH SIX DEGREES OF FREEDOM

Synthesis and research of parallel mechanisms is one of the robotics trend. The work is devoted to the design and experimental study of the parallel mechanism with a constant gear ratio with six degrees of freedom. The drives can provide a ratio of 1:1 with the movement of the output link. The presented mechanism can have wide possibilities of application in industries. The mechanism contains six drives and six kinematic chains. This mechanism has the property of kinematic decoupling of translational and rotational movements. The paper considers the physical model of the mechanism, shows its components and component parts and assemblies. The operability of the developed device has been experimentally tested.

IKFlow: Generating Diverse Inverse Kinematics Solutions

Inverse kinematics—finding joint poses that reach a given Cartesian-space end-effector pose—is a fundamental operation in robotics, since goals and waypoints are typically defined in Cartesian space, but robots must be controlled in joint space. However, existing inverse kinematics solvers return a single solution, in contrast, systems with more than 6 degrees of freedom support infinitely many such solutions, which can be useful in the presence of constraints, pose preferences, or obstacles. We introduce a method that uses a deep neural network to learn to generate a diverse set of samples from the solution space of such kinematic chains. The resulting samples can be generated quickly (2000 solutions in under 10 ms) and accurately (to within 10 millimeters and 2 degrees of an exact solution) and can be rapidly refined by classical methods if necessary.

NESM-γ: An Upper-Limb Exoskeleton With Compliant Actuators for Clinical Deployment

This letter describes the design and characterization of an upper-limb exoskeleton for post-stroke rehabilitation. The platform interacts with the shoulder and elbow of the user through four active joints, driven by series elastic actuators (SEAs) with custom springs to achieve compactness and ease of maintenance. The exoskeleton adopts a passive kinematic chain for aligning the user's and robot joints’ rotation axes, and a quick flipping mechanism to enable dual-side use. The pole-placement method based on the dynamic model of the SEA was used to design the low-level controller, to guarantee torque control precision and stability. The joint load due to the robot's gravity is counteracted by using a feed-forward gravity compensation algorithm. Experimental characterization demonstrates the torque control bandwidth up to 10 Hz and highly transparent behavior of the joints (namely, close to null parasitic impedance) at least up to 2 Hz, showing suitability for rehabilitation purposes.

Robotic micromanipulation: b) grippers for biological objects

Recent progress in the field of microrobotics tightly linked to an ability to grab an object firmly without the damage to the surface and structure. Process of biological object grabbing by microgrippers faces numerous limitations in the mechanical, electric and thermal domains; these limitations varies from case to case with different objects, therefore, analysis in this area was an aim of this review. This paper covers an area of micrometric size biological object manipulation and performs an analysis of used actuators and kinematic chains of the grippers in the sense of their application. Limitations and restriction of microgrippers applications analysed along available publications in numerous recent references as well as their successful implementation history. Paper provides result of analysis as compact big picture, which will be useful for researchers and designers in the area of microrobotics.

THE LEVEL OF DORSIFLEXION IN YOUNG GYMNASTS COMPARED TO YOUNG ATHLETES - PILOT STUDY

Gymnastic training develops strength, flexibility, concentration, balance, precision, and speed. The purpose of the study is to determine if gymnastic preparation leads to an increase in weight-bearing ankle dorsiflexion range of motion in a closed kinematic chain in young artistic gymnasts compared to a different type of sport. The weight-bearing lunge was chosen to measure the dorsiflexion range of motion in the ankle joint in the closed kinematic chain. The first group consists of members of the Slovak national youth team in artistic gymnastics (n-26). The second group consists of members of the Slovak national team in rhythmic gymnastics (n-13). The control group consists of young athletes (n-22). The mean dorsiflexion range of motion in artistic gymnasts was 47.32 ° in the right ankle joint and 44.75 ° in the left ankle joint. The mean dorsiflexion range of motion in rhythmic gymnasts was 44.32 ° in the right ankle joint and 43.41 ° in the left ankle joint. The mean dorsiflexion range of motion in young athletes was 44.27 ° in the right ankle joint and 42.32 ° in the left ankle joint. Results indicate a statistically significant difference in favor of artistic gymnasts compared to rhythmic gymnasts at the right ankle joint (p-0.04). In the left ankle, the two groups did not differ significantly from each other (p-0.38). There was no significant difference between artistic gymnasts and athletes in the right ankle joint (p-0.09) and the left ankle joint (p-0.19). There was no significant difference between rhythmic gymnasts and athletes at the right ankle joint (p-0.38) and the left ankle joint (p-0.24). A greater dorsiflexion range of motion in a closed kinematic chain in the ankle joint was detected in young gymnasts compared to rhythmic gymnasts. There was no significant difference between artistic gymnasts and athletes.

Design and Fabrication of Eight-Legged Spider Using KLANN Mechanism

In the present paper, an attempt has been made to carry out Design and fabrication of eight-legged spider using klann mechanism. A four-revolute (4R) kinematic chain has been chosen for each leg mechanism in order to mimic the leg structure of an insect. Denavit–Hartenberg (D-H) conventions are used to perform kinematic analysis of the eight-legged spider. The direct and inverse kinematic analysis for each leg has been considered in order to develop an overall kinematic model of an eight-legged spider, when it follows a straight path. The problems related to trajectory generation of legs have been solved for both the swing and support phases of the robot. It is important to mention that trajectory generation problem during the support phase has been formulated as an optimization problem and solved using the least squared method. Lagrange-Euler formulation has been utilized to determine the joint torques. The developed kinematic and dynamic models have been examined for tripod gait generation of the eight-legged spider using klann mechanism.

Symmetry Detection and Topological Synthesis of Mechanisms of Powertrains

The function of vehicle powertrains (including hybrid powertrains) is to transmit power from the power source (engine or electric machine) to driving wheels. The planetary gear train (PGT) is a core structure of mechanisms of powertrains. The detection of topological symmetry is helpful for improving the efficiency of mechanism design. In this paper, we present a fully automatic and reliable method for detecting symmetry of plane kinematic chains and extend this method to symmetry detection and the topological design of mechanisms of powertrains. First, the topological model and adjacency matrix are introduced to represent various kinds of plane kinematic chains. Then, the moment matrix of the kinematic chain is established to obtain link groups, based on which we propose an algorithm to generate the unique numerical code of each link and precisely detect the symmetry. Our method is applied to synthesize different kinds of plane kinematic chains and mechanisms, which can improve the design efficiency of mechanisms of powertrains and other mechanical devices.

A novel compound topological invariant for isomorphism detection of planar kinematic chains

Abstract. The isomorphism identification of the kinematic chain (KC) based on graph theory definition has no advantage in efficiency, especially when the number of links in the KCs is large. The topological characteristic constants for isomorphism identification, such as the power value sequence (PVS), least distance matrix sequence (LDMS), and loop number (LN), are proposed. The fourth PVS, the LDMS, and the LN are compared and arranged in descending order, to form a strong complementary chain, which can identify KCs of at least 15 links with 4 degrees of freedom (DOF). The method is applied to the complete atlas of the following: 8-link 1 DOF, 9-link 2 DOF, 10-link 1 DOF, 12-link 1 DOF, 13-link 2 DOF, and 15-link 4 DOF planar single-joint KCs, 6-link 1 DOF and 7-link 1 DOF planetary gear trains, 8-link 1 DOF planar multiple joint KCs, and contracted graphs with up to six independent loops. All results are in agreement with the reported ones in the literature. Thus, the proposed method possesses good versatility and has been verified as being reliable and efficient.

Geometric algebra methods in volumetric accuracy analysis

With the help of plane geometric algebra, we see volumetric errors as pure geometric objects. We use this identification to expand errors with respect to Abbe's principle into the whole working space with respect to some additional conditions. We show that geometric algebra helps us to understand errors in kinematics chains. We demonstrate our approach on a model example.

Improving machining accuracy for a robotic arm with hybrid kinematic chains based on deformation characteristics

Joint deformation greatly influences machining accuracy for a robotic arm. In this paper, the deformation characteristics of the robotic arm with hybrid kinematic chains are investigated to improve its machining accuracy. Firstly, the deformation model of the joints has been established based on the Strain energy method and Castigliano theorem according to the robot structure. Secondly, the deformation influence coefficient (DIC) is defined to investigate the deformation influence of main components on the end-effector, and the deformation characteristics are evaluated by the simulation. Finally, a small size robotic arm prototype is established and robotic drilling comparative experiments are conducted. The theoretical and experimental results show that the machining method can be selected according to the DIC, in which the force can be applied to the components with better stiffness. On the other hand, the deformation of driving components can also be reduced when the DIC cannot be adjusted to meet the accuracy requirement.

Grip position affects upper limb kinematic chain during tennis double-handed backhand topspin strokes: considerations for transitioning tennis grip position technique

ABSTRACT The purpose of this study was to compare the upper limb kinematic chain of tennis players using either an eastern or continental non-dominant grip position during the forward swing of the double-handed backhand stroke. Sixteen right-handed tennis players performed backhands using two non-dominant grip positions (eastern and continental), aiming for two cross-court zones (deep and short). Trajectory data were captured using sixty reflective markers attached to the upper limb and racket using a 12-camera Vicon motion capture system (250 Hz). Peak angular velocity was significantly greater for multiple joint rotations at the dominant shoulder and entire non-dominant limb in the eastern grip. Subsequently, greater peak racket head angular velocity and post-impact ball speed were generated by the eastern grip, while shot accuracy was similar between grip types. There was delayed dominant shoulder peak adduction angular velocity for the continental grip, possibly due to a lack of skill familiarity causing changes in coordinative patterns. Collectively, the non-dominant grip position appears to influence proximal and distal upper limb movement. Future research should explore upper limb segment coordination comparing preferred and non-preferred double-handed backhand techniques and complete inter-disciplinary investigations to understand what grip positions are most effective for individuals to learn double-handed backhands.

Torque Optimization Method of a 3-DOF Redundant Parallel Manipulator Based on Actuator Torque Range

Abstract The small actuator torque range brings advantages for the high-accuracy control of a manipulator. By taking the minimum actuator torque range into account, this paper proposes a novel torque optimization method of a 3-DOF redundantly actuated parallel manipulator for friction stir welding. The dynamic model of the 3-DOF redundant parallel manipulator with four kinematic chains is derived by using the principle of virtual work. The solution of the dynamics is not unique, and the range of four actuator torques constitutes a 4D generalized rectangle. A torque optimization method that minimizes the actuator torque range is presented by determining the generalized 4D rectangle with minimum side length. The proposed optimization method is a global solution corresponding to one trajectory of the moving platform, and it is compared with the least square method which is a local solution corresponding to one pose of the moving platform.