Kinematic Chain Research Articles

Nonlinear error compensation based on the optimization of swing cutter trajectory for five-axis machining

In order to solve the problem of deviation between actual and theoretical machining paths due to the presence of rotation axis in five-axis machining, an interpolation algorithm based on the optimization of swing cutter trajectory and the method of corresponding nonlinear error compensation are proposed. Taking A-C dual rotary table five-axis machine tool as an example, the forward and reverse kinematic model of the machine tool is established according to the kinematic chain of the machine tool. Based on the linear interpolation of rotary axis, the generation mechanism of nonlinear error is analyzed, the modeling methods of cutter center point, and cutter axis vector trajectory are proposed respectively, and the parameterized model of swing cutter trajectory is formed. The formula for the nonlinear error is obtained from the two-dimensional cutter center point trajectory. According to the established model of swing cutter trajectory, the synchronous optimization method of cutter center point trajectory and cutter axis vector trajectory is proposed, and the nonlinear error compensation mechanism is established. First, pre-interpolation is performed on the given cutter location data to obtain a model of the swing cutter trajectory for each interpolated segment. Then, the magnitude of the nonlinear error is calculated based on the parameters of the actual interpolation points during formal interpolation, and the nonlinear error is compensated for the interpolation points where the error exceeds \([\varepsilon ]\). In the VERICUT simulation, the maximum machining error was reduced from 50 to 5 μm by this paper method. In actual machining, the surface roughness of the free-form surface was reduced from 10.5 μm before compensation to 1.8 μm. The experimental results show that the proposed method can effectively reduce the impact of nonlinear errors on processing, and is of high practical value for improving the accuracy of cutter position and the quality of complex free-form machining in five-axis machining.

Hip Strength and Pitching Biomechanics in Adolescent Baseball Pitchers.

Hip strength may influence the energy flow through the kinematic chain during baseball pitching, affecting athlete performance as well as the risk for injury. To identify associations between hip strength and pitching biomechanics in adolescent baseball pitchers during 3 key events of the pitching cycle. Cross-sectional study. Biomechanics laboratory. A total of 26 adolescent male baseball pitchers (age = 16.1 ± 0.8 years, height = 184.29 ± 5.5 cm, mass = 77.5 ± 8.5 kg). The main outcome measure was hip strength (external rotation, internal rotation, flexion, abduction, adduction, and extension). After strength measurements were acquired, motion capture was used to obtain a full-body biomechanical analysis at 3 events during the pitching cycle (foot contact, maximal external rotation, and ball release). We then evaluated these values for associations between hip strength and pitching biomechanics. Scatterplots were examined for linearity to identify an appropriate correlation test. The associations were linear; thus, 2-tailed Pearson correlation coefficients were used to determine correlations between biomechanical metrics. An α level of .01 was chosen. Ten strong correlations were found between pitching biomechanics and hip strength: 8 correlations between hip strength and kinematics at key points during the pitch and 2 correlations of hip strength with peak elbow-varus torque. Several correlations were noted between lower extremity strength and pitching biomechanics. This information provides data that may be used to improve performance or reduce injury (or both) in pitchers. Increased hip strength in adolescent pitchers may both improve performance and decrease the risk of injury.

Kinematic Chain Equivalent Method for Tube Model and Elastodynamic Optimization for Parallel Mechanism Based on Matrix Structural Analysis

The platforms of parallel mechanisms usually suffer vibration loads. In these cases, structure elastodynamic analysis and elastodynamic optimization of parallel mechanisms are important. A tube structure is very common for parallel mechanisms. This work establishes the model of a tube structure based on matrix structural analysis. The kinematic pair equivalent method is used to simulate the surface contact between the inner and outer tubes. The corresponding mass and stiffness matrices are derived through the strain energy minimization method. The reconfigurable legged lunar lander has been used as an example to verify the effectiveness of this method. By adding the mechanism configuration to the optimization process, the equivalent static load method and the desirability approach are combined and modified. A procedure for the multi-objective elastodynamic optimization of parallel mechanisms is proposed. The optimization procedure is implemented on the lander and the results show a reduction in mass and an increase in natural frequency.

Manipulability Optimization of a Rehabilitative Collaborative Robotic System

The use of collaborative robots (or cobots) in rehabilitation therapies is aimed at assisting and shortening the patient’s recovery after neurological injuries. Cobots are inherently safe when interacting with humans and can be programmed in different working modalities based on the patient’s needs and the level of the injury. This study presents a design optimization of a robotic system for upper limb rehabilitation based on the manipulability ellipsoid method. The human–robot system is modeled as a closed kinematic chain in which the human hand grasps a handle attached to the robot’s end effector. The manipulability ellipsoids are determined for both the human and the robotic arm and compared by calculating an index that quantifies the alignment of the principal axes. The optimal position of the robot base with respect to the patient is identified by a first global optimization and by a further local refinement, seeking the best alignment of the manipulability ellipsoids in a series of points uniformly distributed within the shared workspace.

An Analytic and Computational Condition for the Finite Degree-of-Freedom of Linkages, and Its Relation to Lie Group Methods

Abstract The finite degree of freedom (DOF) of a mechanism is determined by the number of independent loop constraints. In this paper, a method to determine the maximal number of loop closure constraints (which is independent of a specific configuration) of multiloop linkages is introduced and applied to calculate the finite DOF. It rests on an algebraic condition on the joint screws, which stems from the analytic condition that minors of certain rank and their higher derivatives vanish. A computational algorithm is presented to determine the maximal rank of the constraint Jacobian in an arbitrary (possibly singular) reference configuration. This algorithm involves screw products of constant screw vectors only. Unlike the Lie group methods for estimating the DOF of so-called exceptional linkages, this method does not rely on partitioning kinematic loops into partial kinematic chains, and it is applicable to multiloop linkages. The DOF computed with this method is at least as accurate as the DOF computed with the Lie group methods. It gives the correct DOF for any (possibly overconstrained) linkage where the constraint Jacobian has maximal rank in regular configurations. The so determined maximal rank has further significance for classifying linkages as being exceptional or paradoxical but also for detecting singularities and shaky linkages.

Association between unilateral functional ankle instability, limited ankle dorsiflexion range of motion and low back pain

There is growing evidence that supports the correlation between incidence of ankle dysfunction and low back pain (LPB). Although the spine and ankle seem like distant regions of the body, they are functionally connected by the lower extremity kinematic chain. The aim of the current study was to investigate the association between functional ankle instability (FAI), limited ankle dorsiflexion (DF) range of motion (ROM) and (LPB). One hundred two subjects with chronic ankle sprain pain participated in this study. The mean ± SD age, weight, height, and BMI of the study group were 43.5 ± 12.96 years, 85.27 ± 14.22 kg, 172.9 ± 8.45 cm, and 28.59 ± 4.72 kg/m². LPB was measured by Visual Analogue Scale (VAS), FAI was measured by the anterior drawer test and DF ROM was measured by the lunge test. All statistical analyses were performed using the Statistical Package for Social Studies (SPSS) version 25 for Windows. There was no statistically significant association between pain and age, pain and BMI, pain, and sex (p > 0.05). There was a statistically significant association between pain and drawer test (odd ratio 5.68, p = 0.02) and a statistically significant association between pain and DF ROM (odd ratio 1.16, p = 0.01). The current study supported previous studies recommending FAI and limited ankle DF ROM as a factor in LPB. The authors suggest conducting similar studies with a larger number of participants and include functional measures scales or questionnaires to increase the validity and generalizability of the results.

A car wheel energy harvesting system regarded as a robotic kinematic chain system

The aim of this article is the mathematical modeling of the car wheel with an energy harvester. The car wheel will be represented as a 3-DoF robotic kinematic chain. The Matlab program has been used to simulate the movement of the car wheel and the movement of the electromagnetic energy harvester located on the tire of the wheel. Simulation of the movement of the energy harvesting element allows us to compute the energy harvested in such a system.

Robotic Tool Tracking Under Partially Visible Kinematic Chain: A Unified Approach

Anytime a robot manipulator is controlled via visual feedback, the transformation between the robot and camera frame must be known. However, in the case where cameras can only capture a portion of the robot manipulator in order to better perceive the environment being interacted with, there is greater sensitivity to errors in calibration of the base-to-camera transform. A secondary source of uncertainty during robotic control are inaccuracies in joint angle measurements which can be caused by biases in positioning and complex transmission effects such as backlash and cable stretch. In this work, we bring together these two sets of unknown parameters into a unified problem formulation when the kinematic chain is partially visible in the camera view. We prove that these parameters are nonidentifiable implying that explicit estimation of them is infeasible. To overcome this, we derive a smaller set of parameters we call lumped error since it lumps together the errors of calibration and joint angle measurements. A particle filter method is presented and tested in simulation and on two real world robots to estimate the lumped error and show the efficiency of this parameter reduction.

Design and Validation of a Cable-Driven Asymmetric Back Exosuit

Lumbar spine injuries caused by repetitive lifting rank as the most prevalent workplace injury in the United States. While these injuries are caused by both symmetric and asymmetric lifting, asymmetric is often more damaging. Many back devices do not address asymmetry, so we present a new system called the Asymmetric Back Exosuit (ABX). The ABX addresses this important gap through unique design geometry and active cable-driven actuation. The suit allows the user to move in a wide range of lumbar trajectories while the “X” pattern cable routing allows variable assistance application for these trajectories. We also conducted a biomechanical analysis in OpenSim to map assistive cable force to effective lumbar torque assistance for a given trajectory, allowing for intuitive controller design in the lumbar joint space over the complex kinematic chain for varying lifting techniques. Human subject experiments illustrated that the ABX reduced lumbar erector spinae muscle activation during symmetric and asymmetric lifting by an average of 37.8% and 16.0%, respectively, compared to lifting without the exosuit. This result indicates the potential for our device to reduce lumbar injury risk.

Deformation prediction and compensation of a dual-machine riveting system for aircraft assembly

Automatic riveting systems play a crucial role in the field of aircraft manufacturing. In the riveting process, the machine tool bears a large axial squeezing force, and the resulting deformation will inevitably affect the riveting quality. In this paper, a dual-machine riveting system is developed first, the kinematic chain model and the lower-numbered body of the system structure are constructed sequentially. Then, considering the interaction and coupling effect of the two machines in the actual riveting process, the relative stiffnesses of the dual machine in the resisting state are identified by loading tests. Based on the stiffness data at a combination of postures within the workspace, a Kriging prediction model is established to describe the relationship between stiffness and postures. According to the prediction results, the influence of rotational and translational axes on the spatial stiffness distribution of the riveting system is revealed. Finally, the online deformation compensation is realized by modifying the displacement of the feed axis on both sides. A riveting experiment is carried out, and the results demonstrate that the riveting quality is significantly improved after compensation.

Design of Pick and Place Robot

The popular concept of a robot is of a machine that looks and works like a human being. The industry is moving from current state of automation to Robotization, to increase productivity and to deliver uniform quality. The industrial robots of today may not look the least bit like a human being although all the research is directed to provide more and more anthropomorphic and humanlike features and super-human capabilities in these. One type of robot commonly used in industry is a robotic manipulator or simply a robotic arm. It is an open or closed kinematic chain of rigid links interconnected by movable joints. In some configurations, links can be considered to correspond to human anatomy as waist, upper arm and forearm with joint at shoulder and elbow. At end of arm a wrist joint connects an end effect which may be a tool and its fixture or a gripper or any other device to work.

Kinematic chains with preserved mobility for arbitrary arrangements of their links

Kinematic chains made from links whose lengths and twist angles satisfy a certain proportionality rule are considered. A notion of exchange symmetry for the links of any such chain affords a new understanding of the mobility of well-known overconstrained mechanisms, exemplified by Bennett’s four-bar linkage, and provides a unifying framework for explaining the mobility of a recently discovered class of nontrivial underconstrained mechanisms. These findings allow for the design of mechanisms consisting of links that can be arbitrarily reordered without altering their number of internal degrees of freedom and, thus, of modular mechanical systems that can be assembled in different ways to serve different purposes. A nine-hinged linkage that can be assembled in ninety-four distinct ways, each evincing a single internal degree of freedom, is presented as an example of such a modular system.

Uncertainty Propagation and Assessment of Five-Axis On-Machine Measurement Error

Abstract As an important technology of adaptive machining, on-machine measurement (OMM) is always used to measure the shape of the to-be-cut surface. Due to the multi-source errors in an OMM system, the confidence of the measurement accuracy becomes particularly important before planning the next cutting procedure. OMM is implemented by multi-components involving machine tools, fixture, and on-machine probe. Each component introduces uncertainty of error into the measurement result. The positioning error, alignment error, and eccentricity error are investigated in terms of the expectation, uncertainty, and probability density function. By the kinematics of the components participated in the measurement, these errors are accumulated to affect the measurement results. Thus, the uncertainty of the final measurement result is determined by the accumulation of uncertainty of error sources. In order to evaluate the uncertainty of measurement error, an uncertainty propagation model involving positioning error of five-axis machine tools, alignment error of workpiece, and eccentricity error of the stylus tip is established in terms of the kinematic chain of OMM. Then, the uncertainty of the measurement result in vector form is obtained. Finally, the simulation and the experiment about the impeller are employed to validate the effectiveness and repeatability of the uncertainty propagation model for five-axis OMM.

An innovative joint-space dynamic theory for rigid multi-axis system-Part Ⅰ: Fundamental principles

This study, being divided into two parts, proposes an innovative joint-space dynamics theory for rigid multi-axis system. This paper, being the first part, demonstrates the fundamental principles and presents the detailed mathematical derivation of explicit inverse dynamic equations. To yield an explicit form of dynamic equations, a fully parameterized kinematic chain symbolic system is introduced. Then the Lagrangian equations are furtherly derived to eliminate the redundant terms. The obtained equation has a concise expression which explicitly contains kinematic parameters, dynamic parameters, and joint variables. Moreover, taking advantage of the explicit expression of dynamic equation, this method has fewer modeling processes which only includes coordinate system establishment, parameter determination and parameter substitution. Finally, the correctness of proposed method is validated by a planar 3-axis manipulator example and a 3-axis Mars Rover rocker arm example.

Observability of the relative motion from inertial data in kinematic chains

Real-time motion tracking of kinematic chains is a key prerequisite in the control of, e.g., robotic actuators and autonomous vehicles and also has numerous biomechanical applications. In recent years, it has been shown that, by placing inertial sensors on segments that are connected by rotational joints, the motion of that kinematic chain can be tracked accurately. These methods specifically avoid using magnetometer measurements, which are known to be unreliable since the magnetic field at the different sensor locations is typically different. They rely on the assumption that the motion of the kinematic chain is sufficiently rich to assure observability of the relative pose. However, a formal investigation of this crucial requirement has not yet been presented, and no specific conditions for observability have so far been given. In this work, we present an observability analysis and show that the relative pose of the body segments is indeed observable under a very mild condition on the motion. We support our results by simulation studies, in which we employ a state estimator that neither uses magnetometer measurements nor additional sensors and does not impose assumptions on the accelerometer to measure only the direction of gravity, nor on the range of motion or degrees of freedom of the joints. We investigate the effect of the amount of excitation and of stationary periods in the data on the accuracy of the estimates. We then use experimental data from two mechanical joints as well as from a human gait experiment to validate the observability criterion in practice and to show that small excitation levels are sufficient for obtaining accurate estimates even in the presence of time periods during which the motion is not observable.

Fault detection and classification in kinematic chains by means of PCA extraction-reduction of features from thermographic images

Kinematic chains are essential elements configurable in different topologies according to the requirements of industry. Their main components are the rotating machines and mechanical parts in which diverse faults can appear. Nowadays, infrared imaging analysis has gained attention for monitoring kinematic chains, however, the approaches for detecting and classifying faults still can be improved. Therefore, this work presents a methodology that uses a low-cost infrared measurement system and combines adequate techniques, such as infrared images preprocessing and segmenting, extraction of statistical indicators, generation of a high-dimensional matrix of features, features reduction, and categorization, for accurately detecting and classifying a wide variety of fault conditions in kinematic chains. This approach was applied to a configurable kinematic chain under the following conditions: healthy motor, misalignment, unbalance, one and two broken rotor bars, bearing faults on the outer race, healthy gearbox, and gearbox wearing. The obtained results validate the effectiveness of the proposed methodology.

Violation of supporting function of feet in children with hip subluxation of dysplastic genesis

Objective. To study the plantographic characteristics of the feet in children with unilateral dysplastic hip subluxation (DHS) and to analyze the patterns of plantar pressure distribution on the affected and intact sides.
 Material and methods. A biomechanical study was conducted in 23 children, aged 13 to 17 years, with unilateral DHS of Crowe group I. The plantographic characteristics of the feet were evaluated and their relationship with the vertical balance of the patients body was analyzed. The control group consisted of 18 healthy children of the same age.
 Results. In patients with unilateral DHS, there is a significant decrease in all indices of support: anterior t, medial m and median s compared with healthy children, not only on the foot of the affected limb, but also on the intact side. It indicates a deterioration in the spring function of the transverse and longitudinal arches of the feet due to their rigidity. The foot on the affected lower limb has a pathologically increased Clarke's angle , which indicates an increase in the height of the longitudinal arches of the foot, which leads to a decrease in the total area of its support. In patients, there is a pathological increase in comparison with the norm of functional relationships between the arches of the foot on the affected and intact lower extremities, that is a sign of a formed pathological foot support strategy.
 Conclusions. The pathological supporting strategy of the feet on the affected and intact lower extremities in patients with unilateral DHS may be a consequence of a violation of the global sagittal balance of the body, leading to an adaptive reaction of the musculoskeletal system in response to compensatory changes in the links of the kinematic chain "spine-pelvis".

Computer-aided digitization method for structural synthesis of planar non-fractioned kinematic chains with pure revolute joints

Structural synthesis plays an important role in the conceptual design of mechanisms. Based on the link assortment array, links are divided into binary links and multi-vertex links. From the relation of binary links and multi-vertex links, a new form of the adjacency matrix is introduced to illustrate planar kinematic chain. It enriches the representative form of the adjacency matrix, which can provide a new direction for rigid-chain detection and structural synthesis. Without auxiliary graph models, based on the link-path adjacency matrix, characteristic code, and Sudoku Crosswords, a computer-aided digitization method is proposed to synthesize the whole family of planar non-fractioned kinematic chains. Compared with most existing methods of structural synthesis, isomorphic kinematic chains and some rigid chains are identified and deleted in the generation of link-path adjacency matrix, which can improve the efficiency of structural synthesis. By synthesizing planar non-fractioned kinematic chains with up to 10 links and 5 degrees of freedom, results confirm that the proposed method is available.

Optimal Synthesis of Loader Drive Mechanisms: A Group Robust Decision-Making Rule Generation Approach

The objective of this paper is to present a novel, hybrid group multi-criteria decision approach that can be used to evaluate alternatives for the optimal synthesis of loader drive mechanisms. In most product design engineering groups, experts have expertise in different areas and robust decision-making is necessary to integrate a number of opposing opinions, attitudes, and solutions. This study presents the application of an integrated approach for decision-making, i.e., the generation of a robust decision-making rule for group decision-making (RDMR-G) by combining different multi-criteria decision-making (MCDM) methods and Taguchi’s robust quality engineering principles. The basic idea behind this article was to create an approach that enables the comprehensive and robust consideration of expert opinions given the existence of numerous objective and subjective methods for determining the criteria weights, which are crucial to the final ranking of alternatives in any decision-making problem. In order to set the optimal configuration of a loader drive mechanism, five experts, all with a high level of experience and knowledge in this field, considered twenty-six different kinematic chain construction solutions, i.e., alternatives, and evaluated them with respect to six criteria. The obtained results and rankings provided by each expert and each criteria weighting method were compared using Kendall’s τb and Spearman’s ρ tests. As an example, this paper demonstrates the practical application of a RDMR-G approach and in doing so contributes to the literature in the fields of product design engineering and decision-making.

ROS 2 Configuration for Delta Robot Arm Kinematic Motion and Stereo Camera Visualization

The Delta robot is one of the robot types that is used in agriculture and industrial application. However, before the complex physical development of the robot, a simulation needs to be developed to ensure the perfect functionality of the design. Therefore, this paper presented a development of simulation for a parallel delta robot using a Robot Operating System 2 (ROS 2) environment and stereo camera visualization. The contribution of this research is to present the development details and the proposed solution to solve issues encountered during the development. The development of script in the format of eXtensible Markup Language (XML), Unified Robot Description Format (URDF), and Simulation Description Format (SDF) are presented for describing a robot's physical structure, allowing a robotic system to be depicted in a tree structure, and defining the delta robot arm, which is made up of closed-loop kinematic chain linkage that will be simulated in Gazebo. For the results, several Gazebo plugin libraries are compared and tested for the wheels motion control, stereo camera visualization, and delta robot arm kinematic motion. From the experiment, the best method is inverse kinematic motion the method is selected and used in the simulation. The selected method resulted in an average percentage error of 3.92%, 3.72%, and 2.92%, respectively for each joint.