Kinematic Chain Research Articles

On the Configurations of Closed Kinematic Chains in Three-dimensional Space

A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three dimensions. We investigate the space of configurations, described in terms of joint angles of its spherical joints, that satisfy the the loop closure constraint, meaning that the kinematic chain is closed. In special cases, we can find a new set of parameters that describe the diagonal lengths (the distance of the joints from the origin) of the configuration space by a simple domain, namely a cube of dimension $n-3$. We expect that the new findings can be applied to various problems such as motion planning for closed kinematic chains or singularity analysis of their configuration spaces. To demonstrate the practical feasibility of the new method, we present numerical examples.

Novel loop tree for the similarity recognition of kinematic chains

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.

The Clinician's Guide to Baseball Pitching Biomechanics.

Improper baseball pitching biomechanics are associated with increased stresses on the throwing elbow and shoulder as well as an increased risk of injury. Previous studies quantifying pitching kinematics and kinetics were reviewed. Clinical review. Level 5. At the instant of lead foot contact, the elbow should be flexed approximately 90° with the shoulder at about 90° abduction, 20° horizontal abduction, and 45° external rotation. The stride length should be about 85% of the pitcher's height with the lead foot in a slightly closed position. The pelvis should be rotated slightly open toward home plate with the upper torso in line with the pitching direction. Improper shoulder external rotation at foot contact is associated with increased elbow and shoulder torques and forces and may be corrected by changing the stride length and/or arm path. From foot contact to maximum shoulder external rotation to ball release, the pitcher should demonstrate a kinematic chain of lead knee extension, pelvis rotation, upper trunk rotation, elbow extension, and shoulder internal rotation. The lead knee should be flexed about 45° at foot contact and 30° at ball release. Corrective strategies for insufficient knee extension may involve technical issues (stride length, lead foot position, lead foot orientation) and/or strength and conditioning of the lower body. Improper pelvis and upper trunk rotation often indicate the need for core strength and flexibility. Maximum shoulder external rotation should be about 170°. Insufficient external rotation leads to low shoulder internal rotation velocity and low ball velocity. Deviation from 90° abduction decreases the ability to achieve maximum external rotation, increases elbow torque, and decreases the dynamic stability in the glenohumeral joint. Improved pitching biomechanics can increase performance and reduce risk of injury. Level C.

Studying the possibility of controlling the dynamic state of an impact ripper

Introduction. Vibratory and impact loads transferred to the operator workplace limit the efficiency enhancement of rock or firm ground preparatory destruction by impact ripping equipment. One way to reduce the dynamic load transfer to the base machine and the operator is to include additional links into the implement kinematic chain, which redistribute dynamic loads to the zone of rock mass destruction. Methods of research are based on an integrated and systematic approach to the object of study as a multi-mass system, the state of which depends on the physical and mechanical properties of the medium, technological and structural factors affecting the energy efficiency of the mining and earthworks process. The research focuses on analyses of the effect the additional links parameters have on dynamic loads redistribution to the zone of rock or firm ground destruction. The research focus is conditioned by the need to develop structural solutions for the work equipment that controls the dynamic state of technological systems. When the constructive modernization solutions are completely exhausted, the need to improve the existing equipment and develop the fleet for special mining and earthworks necessitate such studies. Results. Removing the impact tool beyond the limits of the attachment point on the base machine is considered as one of the possible ways to protect the base machine and the operator from vibration loads. For this reason, the work equipment design provides for a rod with a counterweight pivotally connected to a toolbar. Force balance equations, including inertia forces as well, were derived considering the dynamic load impact. A relationship has been established between the impact tool layout on the rod, the impact energy and the reactive force in the rod rotation support. Conclusions. Graphical dependencies analysis established the range of variable parameters, which ensure the energy-efficient operation of the ripping equipment with a minimum transfer of dynamic loads to the operator’s workplace.

An algorithm for trajectory optimization of dual-arm coordination based on arm angle constraints

In this paper, the motion planning of a dual-arm robot with kinematic constraints is studied based on arm-angle constraints. When a dual-arm robot moves a common object, a closed kinematic chain is formed between the dual-arm and the object. The standard sampling-based trajectory planning algorithm solves the problem with closed-chain constraint, but this causes other problems; the running time increases, the success rate decreases, and the motion trajectory of the end effector is not smooth resulting in large output error. Therefore, this paper proposes a dual-arm coordinated trajectory optimization algorithm based on arm-angle constraints. Firstly, the kinematics of the dual-arm robot is modeled and analyzed, and the definition of the arm-angle in a seven-axis robot is proposed, the workspace of the dual-arm coordinated operation is considered to constrain it, the kinematics equation combined with the single/multi-objective optimization algorithm is used to optimize the end output error, and the joint trajectory is parameterized. This paper solves the problems that the slave arm lags behind the main arm, the motion trajectory of the dual-arm is not smooth, and the dual-arm are squeezed due to internal force during the coordinated movement of the dual-arm. The trajectory optimization improves the synchronization of the coordinated operation of the dual-arm, reduces the output error of the velocity and acceleration at the end of the dual-arm. After limiting the arm-angle, dual-arm manipulation is anthropomorphic the robot does not produce distorted arm configurations.

ПОСТРОЕНИЕ РАЦИОНАЛЬНЫХ ПЛАНЕТАРНЫХ МЕХАНИЗМОВ НА ОСНОВЕ МАТРИЧНОГО МЕТОДА СТРУКТУРНОГО АНАЛИЗА

The study objective is to show the possibilities of the matrix approach in solving problems of analyzing structural properties and developing efficient structures of mechanisms.
 The task to which the paper is devoted is to define the structural characteristics of planetary gears with one external and one internal engagement and to improve their structures.
 Research methods. The paper uses a matrix method for analyzing the structural properties of the mechanism and modifying its structure, which is based on describing the mobility of kinematic pairs, links, kinematic chains, mechanisms using mobility matrices and the use of matrix equations. 
 The novelty of the work. Matrix equations are proposed that make it possible to conduct a structural analysis of independent closed circuits of complex mechanisms consistently. In contrast to the algebraic method, using a matrix approach, it is possible not only to find local and general mobility, determine the number of redundant connections, but also to find which mobility is missing.
 Study results. The analysis showed that the planetary gears under consideration have redundant connections and mobility in the gears, leading to point contact of the teeth and uneven load distribution in planetary pinions. Proposals have been developed to eliminate redundant connections identified in the mechanisms.
 Conclusions. The study conducted on the example of planetary gears shows that the matrix method of structural analysis is an effective means of identifying redundant connections and a tool that simplifies the search for technical solutions to eliminate them.

Innovative design method for planar mechanism configuration based on component similarity discrimination

Abstract. Obtaining new models of mechanical equipment to conduct mechanical innovative design through kinematic chain configuration synthesis is an effective method. However, in practice, due to the existence of similar components, existing innovative design methods easily produce redundant design schemes, which require extensive isomorphic discrimination operations, and the design process is complex. In view of existing problems, this study analyzes a method for discriminating between similar components of mechanisms from the perspective of graph theory and then applies it to the specialization of topological graphs to solve the problem of redundant design schemes. Finally, using the innovation of a drilling rig drilling arm mechanism as an example, 52 feasible schemes without redundancy are obtained. This paper provides a reference for the innovation of the configuration of planar mechanisms without design redundancy.

Design, rapid manufacturing and modeling of a reduced-scale forwarder crane with closed kinematic chain

Forestry cranes are of paramount importance in forestry operations, so considerable efforts have been carried out to improve their performance in recent years. However, all these efforts have focused on automation technology, leaving aside other alternatives for improvement. Among these alternatives is model-based design, which has the potential to be game-changing for the forest industry. Because research on model-based design is almost non-existent for forestry cranes, there are many gaps that should be filled before presenting improved designs of forestry cranes. The purpose of this article is to fill two of those gaps: (1) the high cost-benefit ratio and safety concerns when testing new designs, components or algorithms in industrial-scale forestry cranes and (2) the dynamic modeling of forestry cranes as mechanical systems with closed kinematic chain. Under these premises, this article first presents a reduced-scale platform resembling a forwarder crane with closed-kinematic chain, where the components of the mechanical structure are manufactured with 3D printing technology, and second, the modeling and experimental validation of the reduced-scale forwarder, where the closed kinematic chain is considered as a system of multiple constrained open kinematic chains. For the experimental validation, a comparison between both experimental and simulation results is presented. Results presented in this article broaden the options to design and test new concepts and/or technology to improve forestry cranes performance.

Supra-threshold vibration applied to the foot soles enhances jump height under maximum effort.

Previous studies have shown that absence or reduction of cutaneous sensory feedback can diminish human motor performance under maximum effort. However, it has not been explored whether any appropriate intervention in the cutaneous sensory input can augment the output motor performance, particularly in motor tasks such as jumping that involve the kinematic chain of the entire body. Using shoes with active vibrating insoles, we applied mechanical vibration to the soles of 20 young and healthy adults and evaluated the change in the jump height and muscle activation using within-participants repeated measures. The noise-like vibration having an amplitude of 130% of the sensory threshold of each participant led to an average increase of 0.38 cm in the jump height (p = 0.008) and activation of the rectus femoris of the dominant leg (p = 0.011). These results indicate that application of a properly designed cutaneous stimulus to the soles, the distal end effectors of motor tasks, can augment the output performance by involving the prime movers distant from the end effector.

An efficient combined local and global search strategy for optimization of parallel kinematic mechanisms with joint limits and collision constraints

The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder–Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect of the dimension of the optimization problem and the different constraints are discussed to highlight the complexities of closed-loop kinematic chain optimization. The work also presents the approaches used to consider constraints for passive joint boundaries as well as singularities to avoid internal collisions in such mechanisms. The proposed algorithm can also optimize the length of the prismatic actuators and the constraints can be added in modular fashion, allowing to understand the impact of given criteria on the final result. The application of the presented approach is used to optimize two PKMs of different degrees of freedom.

TelePhysicalOperation: Remote Robot Control Based on a Virtual “Marionette” Type Interaction Interface

Teleoperation permits to control robots from a safe distance while performing tasks in a remote environment. Kinematic differences between the input device and the remotely controlled manipulator or the existence of redundancy in the remote robot may pose challenges in moving intuitively the remote robot as desired by the human operator. Motivated by the above challenges, this work introduces TelePhysicalOperation, a novel teloperation concept, which relies on a virtual physical interaction interface between the human operator and the remote robot in a manner that is equivalent to a “Marionette” based interaction interface. With the proposed approach, the user can virtually “interact” with the remote robot, through the application of virtual forces, which are generated by the operator tracking system and can be then selectively applied to any body part of the remote robot along its kinematic chain. This leads to the remote robot generating motions that comply with the applied virtual forces, thanks to the underlying control architecture. The proposed method permits to command the robot from a distance by exploring the intuitiveness of the “Marionette” based physical interaction with the robot in a virtual/remote manner. The details of the proposed approach are introduced and its effectiveness is demonstrated through a number of experimental trials executed on the CENTAURO, a hybrid leg-wheel platform with an anthropomorphic upper body.

Comparative Analysis of Optoelectronic Accuracy in the Laboratory Setting Versus Clinical Operative Environment: A Systematic Review

Study Design:Systematic review.Objectives:The optoelectronic camera source and data interpolation process serve as the foundation for navigational integrity in robotic-assisted surgical platforms. The current systematic review serves to provide a basis for the numerical disparity observed when comparing the intrinsic accuracy of optoelectronic cameras versus accuracy in the laboratory setting and clinical operative environments.Methods:Review of the PubMed and Cochrane Library research databases was performed. The exhaustive literature compilation obtained was then vetted to reduce redundancies and categorized into topics of intrinsic accuracy, registration accuracy, musculoskeletal kinematic platforms, and clinical operative platforms.Results:A total of 465 references were vetted and 137 comprise the basis for the current analysis. Regardless of application, the common denominators affecting overall optoelectronic accuracy are intrinsic accuracy, registration accuracy, and application accuracy. Intrinsic accuracy equaled or was less than 0.1 mm translation and 0.1 degrees rotation per fiducial. Controlled laboratory platforms reported 0.1 to 0.5 mm translation and 0.1 to 1.0 degrees rotation per array. Accuracy in robotic-assisted spinal surgery reported 1.5 to 6.0 mm translation and 1.5 to 5.0 degrees rotation when comparing planned to final implant position.Conclusions:Navigational integrity and maintenance of fidelity of optoelectronic data is the cornerstone of robotic-assisted spinal surgery. Transitioning from controlled laboratory to clinical operative environments requires an increased number of steps in the optoelectronic kinematic chain and error potential. Diligence in planning, fiducial positioning, system registration and intra-operative workflow have the potential to improve accuracy and decrease disparity between planned and final implant position.

Efficient Analytical Derivatives of Rigid-Body Dynamics Using Spatial Vector Algebra

An essential need for many model-based robot control algorithms is the ability to quickly and accurately compute partial derivatives of the equations of motion. State of the art approaches to this problem often use analytical methods based on the chain rule applied to existing dynamics algorithms. Although these methods are an improvement over finite differences in terms of accuracy, they are not always the most efficient. In this paper, we contribute new closed-form expressions for the first-order partial derivatives of inverse dynamics, leading to a recursive algorithm. The algorithm is benchmarked against chain-rule approaches in Fortran and against an existing algorithm from the Pinocchio library in C++. Tests consider computing the partial derivatives of inverse and forward dynamics for robots ranging from kinematic chains to humanoids and quadrupeds. Compared to the previous open-source Pinocchio implementation, our new analytical results uncover a key computational restructuring that enables efficiency gains. Speedups of up to 1.4x are reported for calculating the partial derivatives of inverse dynamics for the 50-dof Talos humanoid.

Current and Stray Flux Combined Analysis for the Automatic Detection of Rotor Faults in Soft-Started Induction Motors

Induction motors (IMs) have been extensively used for driving a wide variety of processes in several industries. Their excellent performance, capabilities and robustness explain their extensive use in several industrial applications. However, despite their robustness, IMs are susceptible to failure, with broken rotor bars (BRB) being one of the potential faults. These types of faults usually occur due to the high current amplitude flowing in the bars during the starting transient. Currently, soft-starters have been used in order to reduce the negative effects and stresses developed during the starting. However, the addition of these devices makes the fault diagnosis a complex and sometimes erratic task, since the typical fault-related patterns evolutions are usually irregular, depending on particular aspects that may change according to the technology implemented by the soft-starter. This paper proposes a novel methodology for the automatic detection of BRB in IMs under the influence of soft-starters. The proposal relies on the combined analysis of current and stray flux signals by means of suitable indicators proposed here, and their fusion through a linear discriminant analysis (LDA). Finally, the LDA output is used to train a feed-forward neural network (FFNN) to automatically detect the severity of the failure, namely: a healthy motor, one broken rotor bar, and two broken rotor bars. The proposal is validated under a testbench consisting of a kinematic chain driven by a 1.1 kW IM and using four different models of soft-starters. The obtained results demonstrate the capabilities of the proposal, obtaining a correct classification rate (94.4% for the worst case).

Diagnostics of Articular Cartilage Damage Based on Generated Acoustic Signals Using ANN-Part I: Femoral-Tibial Joint.

Osteoarthritis (OA) is a chronic, progressive disease which has over 300 million cases each year. Some of the main symptoms of OA are pain, restriction of joint motion and stiffness of the joint. Early diagnosis and treatment can prolong painless joint function. Vibroarthrography (VAG) is a cheap, reproducible, non-invasive and easy-to-use tool which can be implemented in the diagnostic route. The aim of this study was to establish diagnostic accuracy and to identify the most accurate signal processing method for the detection of OA in knee joints. In this study, we have enrolled a total of 67 patients, 34 in a study group and 33 in a control group. All patients in the study group were referred for surgical treatment due to intraarticular lesions, and the control group consisted of healthy individuals without knee symptoms. Cartilage status was assessed during surgery according to the International Cartilage Repair Society (ICRS) and vibroarthrography was performed one day prior to surgery in the study group. Vibroarthrography was performed in an open and closed kinematic chain for the involved knees in the study and control group. Signals were acquired by two sensors placed on the medial and lateral joint line. Using the neighbourhood component analysis (NCA) algorithm, the selection of optimal signal measures was performed. Classification using artificial neural networks was performed for three variants: I—open kinetic chain, II—closed kinetic chain, and III—open and closed kinetic chain. Vibroarthrography showed high diagnostic accuracy in determining healthy cartilage from cartilage lesions, and the number of repetitions during examination can be reduced only to closed kinematic chain.

Assembly-free design for additive manufacturing of articulated components based on layered precision assignment

ABSTRACT This paper presents an assembly-free design method for additive manufacturing (AM) of articulated components based on layered precision assignment (LPA). The articulated components are top-down decomposed into physically separated or nearly disconnected entities in different types of fit with specific clearance, for layered slicing hereafter. The forward design method sequentially integrates build orientation, adaptive slicing, trajectory optimization, in conjunction with machine uncertainty of 3D printing (3DP). Besides geometric analysis, the machine uncertainty owing to vibration and thermal coupling is considered by establishing general precision model of kinematic chain errors. By utilizing integrated digital twins (DT), the material extruding process can be visualized synchronously during fabrication process, with the support of a series of online sensor metadata. The manufacturing precision at each layer can be allocated and assigned with accurate distribution, on the basis of trajectory error assessment. The physical experiment of human lumbar vertebrae is carried out to verify the proposed method. The experiment proves that the proposed LPA is fundamentally adaptive to non-assembly 3DP of a variety of even alternative processes with multi-materials under machine uncertainty.

Proprioceptive function of the cruciate complex of the knee joint (literature review)

The question of the role of proprioceptive sensitivity in ensuring the normal kinematics of the joints, including the knee, has increasingly attracted the attention of researchers in recent decades. The position on the significance of intra-articular receptors and the concept of proprioception are not new [2, 3]. At the end of the 19th century, Duchenne was one of the first to point out the clinical significance of articular sensitivity. The term "proprioception" was introduced by Sherrington in 1906 [57]. Abbott et al. [4] and Gardner [27] found that the ligaments of the knee joint have a rich sensory innervation that acts as the first link in the kinematic chain. Abbott noted that the impulses that arise in the ligaments are transmitted through the central nervous system to the muscles and this allows you to establish normal, uniform, coordinated movements. Pathologically strong impulses arising from excessive stretching of the ligaments cause contraction of the conjugate muscle group, thereby preventing damage to the soft tissue component of the knee joint.

Geometrically constrained path planning for robotic grasping with Differential Evolution and Fast Marching Square

AbstractThis paper presents a new approach for geometrically constrained path planning applied to the field of robotic grasping. The method proposed in this paper is based on the Fast Marching Square (FM $\, ^2$ ) and a path calculation approach based on an optimization evolutionary filter named Differential Evolution (DE). The geometric restrictions caused by the link lengths of the kinematic chain composed by the robot arm and hand are introduced in the path calculation phase. This phase uses both the funnel potential of the surroundings created with FM $\, ^2$ and the kinematic constraints of the robot as cost functions to be minimized by the evolutionary filter. The use of an optimization filter allows for a near-optimal solution that satisfies the kinematic restrictions, while preserving the characteristics of a path computed with FM $\, ^2$ . The proposed method is tested in a simulation using a robot composed by a mobile base with two arms.

Substantiations of the beginnings of a unified theory of planetary gears

Multi-satellite planetary mechanisms are analyzed. A new approach to the creation of planetary gearboxes on the principle of L. V. Assur's mechanisms is proposed, according to which the satellites add a group of links of zero mobility to the kinematic chain. Schemes of patented multi-satellite planetary gears are shown. The basis for the development of a new theory of design and manufacture of planetary gearboxes is presented. Keywords: planetary gear, satellite, multi-satellite transmission, uniform load distribution, gear transmission. tmmiok@yandex.ru, tmmiok@yandex.ru

Representation of planar kinematic chains with multiple joints based on a modified graph and isomorphism identification

The representation and isomorphism identification of kinematic chains (KCs) with multiple joints are crucial issues to be solved in mechanism research. In this paper, a modified graph—planar face graph (PF graph), is proposed. As a key concept, “face” has been put forward to represent the case that a single, specific relationship is incident with multiple incidents. Some other basic concepts relating to PF graph are also explained in detail. PF graph is used to represent KCs with multiple joints and it reflects the uniqueness of KCs and realizes the one-to-one correspondence between KCs and adjacency and incident matrices. It also establishes relationships with other methods for representing KCs and it is proved to be suitable for complex mechanical systems. Moreover, the sufficient and necessary condition of isomorphism are derived, and two properties of permutation similarity are analysed. Based on them, the modified eigenvalue eigenvector method and the maximum path method are proposed, and they are integrated to form a new algorithm. In addition, the reliability and efficiency of the algorithm are proved.