Kinematic Function Research Articles

COMPARATIVE ANALYSIS OF THE TREATMENT OF PATIENTS WITH DYSPLASTIC AND IDIOPATHIC OSTEOARTHROSIS OF THE HIP JOINT

Hip arthroplasty is a reliable and quick way to relieve the patient of pain, restore movement in the hip joint and improve the function of the affected limb, but the question of how effective this intervention is in dysplastic or idiopathic coxarthrosis requires further study. The objective of the study was to evaluatethe effectiveness of treatment of patients with idiopathic and dysplastic coxarthrosis, and the effect of endoprosthetics on the work of the pelvic muscles. Methods. A comparative analysis of the treatment of 121 patients was conducted, which were divided into two groups — with dysplastic coxarthrosis(63 patients) and with idiopathic coxarthrosis (58 patients). The functional results of the treatment were studied according to the Harris scale, the data of stabilographic studies and the evaluation of the work of the muscles of the pelvic girdle, which are responsible for maintaining the horizontal balanceof the pelvis. Results. In general, the results of endopros thesis were evaluated as good in both groups. At the same time, the average results in the group of patients with idiopathic coxarthrosis are significantly better (t = 2.08; p = 0.001) than in the group of patients with dysplastic coxarthrosis. However, the indicators of the muscles that ensure the horizontal balance of the pelvis, in most cases, remain reduced within 6–8 months after the endoprosthesisoperation. This is evidenced by clinical data and statistical research data. Conclusions. Endoprosthesis of the hip joint is an effective method of coxarthrosis and allows to significantly improve both the patientʼs support and kinematic function and his quality of life. The results of treatment of patients withidiopathic coxarthrosis according to the Harris scoring scale are significantly better than the results of treatment of patients with dysplastic coxarthrosis. But the performance indicators of the muscles of the pelvic girdle, in most cases remain reduced within 6–8 months after endoprosthesis surgery in patientsof both groups.

Clinical efficacy and kinematic analysis of Chinese knotting technique-assisted posterior cruciate ligament reconstruction: A retrospective analysis.

To investigate the clinical efficacy and knee joint kinematic changes of posterior cruciate ligament (PCL) reconstruction assisted by Chinese knotting technique (CKT). A retrospective analysis was conducted on 88 cases of PCL reconstructive surgery admitted between September 2016 and September 2020. All patients were operated on by the same senior doctor and his team. The patients were divided into 2 groups according to whether the CKT was applied, with 44 cases in each group. Both groups received active rehabilitation treatment after surgery. All patients were followed up for more than 2 years. International knee documentation committee, hospital for special surgery (HSS), and Lysholm scores were used to evaluate the clinical efficacy of the 2 methods at 3, 12, and 24 months after surgery. The motion cycle and kinematic indices of the knee joint were measured by the Opti_Knee three-dimensional motion measurement system before surgery and at 3, 12, and 24 months after surgery. A secondary arthroscopic examination was performed at 12 months after surgery, MAS score was used to evaluate the secondary endoscopic examination of PCL. All the patients had wound healing in stage I without infection. International Knee in both sets Documentation Committee scores, HSS scores and Lysholm scores were gradually improved at all time points (P < .05); compared with the traditional group, the HSS score was higher in the reduction group 12 months after surgery (P < .05), but there was no significant difference at 24 months after surgery. 12 months and 24 months after 3 dimensional motion measurement system using Opti_Knee showed a reduction group before and after displacement and displacement of upper and lower range than the traditional group (P < 0. 05). One year after surgery, the good and good rate of MAS score reduction group was higher than traditional group. CKT assisted PCL reconstruction can improve the subjective function score of the affected knee joint and the results of secondary microscopy. Satisfactory knee kinematic function can be obtained in the early stage, and the anteroposteric relaxation of the knee joint can be reduced.

Effects of Virtual Reality Therapy Combined With Conventional Rehabilitation on Pain, Kinematic Function, and Disability in Patients With Chronic Neck Pain: Randomized Controlled Trial.

Neck pain is a common condition that leads to neck motor dysfunction and subsequent disability, with a significant global health care burden. As a newly emerging tool, virtual reality (VR) technology has been employed to address pain and reduce disability among patients with neck pain. However, there is still a lack of high-quality studies evaluating the efficacy of VR therapy combined with conventional rehabilitation for patients with chronic neck pain, particularly in terms of kinematic function. This study aims to investigate the effect of VR therapy combined with conventional rehabilitation on pain, kinematic function, and disability in patients with chronic neck pain. We conducted an assessor-blinded, allocation-concealed randomized controlled trial. Sixty-four participants experiencing chronic neck pain were randomly allocated into the experimental group that underwent VR rehabilitation plus conventional rehabilitation or the control group receiving the same amount of conventional rehabilitation alone for 10 sessions over 4 weeks. Pain intensity, disability, kinematic function (cervical range of motion, proprioception, and mean and peak velocity), degree of satisfaction, and relief of symptoms were evaluated at 3 timepoints (baseline, postintervention, and at 3 months follow-up). A 2*3 mixed repeated measures analysis of variance was utilized for analyzing the difference across indicators, with a significant difference level of .05. Both groups demonstrated significant improvements in pain, disability, and kinematic functions (P<.05) at postintervention and at 3-month follow-up. The experimental group showed superior therapeutic outcomes compared to the control group in pain reduction (mean difference from the baseline: 5.50 vs 1.81 at posttreatment; 5.21 vs 1.91 at the 3-month follow-up, respectively; P<.001), disability improvement (mean difference from baseline: 3.04 vs 0.50 at posttreatment; 3.20 vs 0.85 at the 3-month follow-up, respectively; P<.001), and enhanced kinematic functions (P<.05). Moreover, participants in the experimental group reported better satisfaction and relief of symptoms than the control group (P<.05), with better initiative for exercising during the follow-up period. However, there was no between-group difference of improvement in proprioception. No adverse events were reported or observed in our research. The findings of our study support the efficacy of combining VR therapy with conventional rehabilitation in alleviating pain, enhancing kinematic function, and reducing disability of patients with chronic neck pain. Future research should focus on refining the therapeutic protocols and dosages for VR therapy as well as on optimizing its application in clinical settings for improved convenience and effectiveness. Chinese Clinical Trial Registry ChiCTR2000040132; http://www.chictr.org.cn/showproj.aspx?proj=64346.

Dysphagia Pattern in Early to Moderate Parkinson's Disease Caused by Abnormal Pharyngeal Kinematic Function.

Airway invasion is common in patients with Parkinson's disease (PD) and can cause serious complications. However, a PD-related dysphagic pattern has not been clearly elucidated. In this study, 53 patients with early to moderate PD were enrolled to undergo a videofluoroscopic study of swallowing evaluation (VFSS) and a battery of neuropsychological assessments. A set of VFSS variables (three visuoperceptual, nine temporal, and six spatial) were measured. The main effects of bolus viscosity and volume on airway invasion were calculated. Statistical analyses were performed to determine key kinematic factors of airway invasion for swallowing each bolus type. Airway invasion frequency was significantly higher for liquid boluses (liquid vs. pudding P < 0.001; liquid vs. honey P = 0.006). Laryngeal vestibule closure reaction time (LVCrt) was the key kinematic factor of airway invasion for 3ml liquid swallow (P = 0.040), anterior displacement of hyoid bone was the key kinematic factor for both 5ml and 10ml liquid swallows (P = 0.010, 0.034, respectively). Male sex and advanced Hoehn and Yahr stage were significantly related to reduced anterior displacement of hyoid bone. These results reveal the dysphagic pattern related to PD, demonstrating that prolonged LVCrt and reduced anterior displacement of hyoid bone are two crucial kinematic factors contributing to airway invasion during the liquid swallow. In addition, hyoid bone dysfunction was correlated with disease severity and male sex. Our findings warrant further investigation of the pathophysiological mechanism of dysphagia in PD and would guide clinical intervention.

Differential Studies of Argon Particle and Antiparticle Interactions: Present Status and Future Possibilities

Although the comparison of fully differential ionization data for particle and antiparticle impact provides the ultimate tests of theoretical models, only very low antiparticle beam intensities are available. Hence, few experiments of this type have been performed. Therefore, available experimentally obtained single and double differential cross-sections, which are much easier to obtain, are compared in order to demonstrate differences when only the projectile mass or charge (+1 or −1) is changed. Included in the comparison are cross-sections calculated for positron and electron impact using a three-particle classical trajectory Monte Carlo method. The calculated cross-sections provide independent information about the ejected electron and the scattered projectile contributions, plus information about the impact parameters, all as functions of the collision kinematics. From these comparisons, suggestions as to where future investigations are both feasible and useful are provided.

Numerical investigation of sandwich plate in bending by a new inverse shear deformation theory based on finite element analysis

Employing innovative kinematic function, a new inverse trigonometric shear deformation theory (nITSDT), variationally suitable, is developed to acquire pertinent data on the bending of sandwich plates subjected to transverse loads with variable aspect ratios(S). This nITSDT eliminates the need for shear correction factors since the transverse shear stress is directly determined by constitutive relations on the two extreme faces of sandwich plate satisfying the shear stress free surface circumstances. The governing equations and boundary conditions of the nITSDT are obtained by applying the dynamic version of the virtual work principle. For sandwich plates with simplly supports, solution is given by MATLAB code using Finite Element (FE) based on nITSDT. The findings of displacements and stresses are supported by those of more comprehensive theories, and the exact solution serves to highlight the viability of the proposed theory.

A general leading-order asymptotic theory of thin microstructural plates and uncertainty quantification of the elastic performance of composite laminates

We propose an asymptotic framework that may be used as a platform to model general thin microstructural plates, and our initiative is twofold. First, it provides an explanation to why so many tailored plate theories have been introduced for modelling plates bearing microstructures. In hypotheses-based plate theories, the microstructural details within each ply are usually smeared out. But it is shown that with such in-ply details properly taken into account, one manages to address, even only with leading-order terms, several key issues, such as transverse shear strain effects, shear locking, etc., whose rationalisation is believed to necessitate higher-order terms. To a certain degree, the proposed formulation can be used as a target for tailoring kinematic shape functions in both Reissner-Mindlin types of plate theories and zig-zag theories. Second, being slender in nature, a microstructural plate should accommodate a stress state that is close to the state of plane stress. This agrees with our findings that the (leading-order) mechanical units of a microstructural plate should be two-dimensional slices parameterised with the thickness coordinate, distinguishing the proposed framework from other plate theories based on asymptotic analysis. To demonstrate what the present framework can predict beyond existing theories, the effects on the behaviour of fibrous laminates due to manufacturing uncertainties are investigated.

Virtual Reality Intervention for Patients With Neck Pain: Systematic Review and Meta-analysis of Randomized Controlled Trials.

Neck pain is a prevalent condition that causes an enormous health care burden due to the lack of efficient therapies. As a promising technology, virtual reality (VR) has shown advantages in orthopedic rehabilitation. However, there is no meta-analysis evaluating the effectiveness of VR in neck pain management. This study aims to review original randomized controlled trials (RCTs) evaluating the effectiveness of VR for neck pain and to provide evidence for the clinical application of a new alternative approach for pain management. A total of 9 electronic databases were systematically searched for relevant articles published from inception to October 2022. RCTs in English or Chinese that investigated VR therapy for participants with neck pain were included. The methodological quality and the evidence level were assessed using the Cochrane Back and Neck Risk of Bias tool and the Grading of Recommendations Assessment, Development, and Evaluation (GRADE) guideline, respectively. A total of 8 studies with 382 participants were included for the final analysis. For the pain intensity, the overall pooled effect size was 0.51, with a standardized mean difference (SMD) of -0.51 (95% CI -0.91 to -0.11; GRADE: moderate), favoring VR therapy compared with controls. Subgroups analyses revealed that significant differences in pain intensity were found in the multimodal intervention (VR in combination with other therapies) than in other interventions (SMD -0.45, 95% CI -0.78 to -0.13; GRADE: moderate), and better analgesic effects were also observed in patients with chronic neck pain receiving VR intervention (SMD -0.70, 95% CI -1.08 to -0.32; GRADE: moderate) and patients treated in the clinic or research unit (SMD -0.52, 95% CI -0.99 to -0.05; GRADE: moderate) than controls. Regarding other health outcomes, the VR experienced less disability, lower kinesiophobia, and greater kinematic function (cervical range of motion, mean and peak velocity). Nevertheless, the follow-up effects of VR therapy on pain intensity and disability were not found. Existing moderate evidence support VR as a beneficial nonpharmacological approach to improve pain intensity in patients with neck pain, with advantages to multimodal intervention, people with chronic neck pain, and clinic or research unit-based VR therapy. However, the limited quantity and high heterogeneity of the articles limit our findings. PROSPERO CRD42020188635; https://tinyurl.com/2839jh8w.

Automatic Control System of Manipulator Clamping Angle Based on Machine Vision

In order to shorten the time it takes for the manipulator components to reach the preset position and avoid the behavior state of excessively increasing the gripping angle, an automatic control system for the gripping angle of the manipulator based on machine vision is designed. According to the motion state of the mechanical components of the gripper, the connection sensitivity of the angular position sensor is controlled, and then the tension and pressure control structure is used to complete the on-demand adjustment of the clamping force action form and realize the construction of the application platform environment of the hardware structure of the automatic control system. On this basis, by grabbing the necessary manipulator operation image, following the principle of machine vision, completing the preprocessing, and then combining the kinematic functions to perform the force control switching operation and realizing the gripping force control based on machine vision, and completing the design and application of the automatic control system for the gripping angle of the manipulator. The experimental results show that when the motor driving speed is equal to 2000 PPS,4000 PPS, and 6000 PPS, the consumption time required for the manipulator components to reach the preset position will not exceed 9.5s. Compared with the double closed-loop control system, it is more in line with the application requirements of effectively controlling the behavior of the clamping angle.

Effectiveness of Therapeutical Interventions on the Scapulothoracic Complex in the Management of Patients with Subacromial Impingement and Frozen Shoulder: A Systematic Review

Shoulder pain is one the most common musculoskeletal complaints. The most common pathological causes of shoulder pain in the general population are subacromial impingement syndrome and adhesive capsulitis, commonly referred to as "frozen shoulder". The purpose of this study was to evaluate the role of the scapulo-thoracic complex, particularly in scapular kinematic functions, in rehabilitative interventions for shoulder pain in patients suffering from these two common conditions. This systematic review was performed using the scientific search engines PubMed, PEDro and Cochrane Library, considering only randomized controlled clinical trials. Selected articles were evaluated according to the level of evidence and methodological quality. Thirteen randomized clinical trials were selected. Interventions have been divided into three macro-categories: (1) manual therapy in patients with subacromial impingement, (2) therapeutic exercise programs including interventions on the scapulothoracic complex in patients with subacromial impingement syndrome, and (3) therapeutic exercise programs including interventions on the scapulothoracic complex in patients with frozen shoulder. Following this, a qualitative analysis was performed according to outcomes such as pain, shoulder function, and scapular kinematics. Physiotherapy exercise programs that included scapular motor control training and scapular mobilizations, in particular, those of the scapulo-thoracic complex in scapular kinematic function, represent valid alternatives in the management of patients with subacromial impingement syndrome.

A tilting system design and simulation of ground penetrating radar

In this paper, a tilting system of ground penetrating radar by 5R1C 6-bar linkage mechanism is proposed. The kinematic function of hydraulic cylinder and the output angle is given in explicit format. The quasi-static formulation of the tilting system is proposed to calculate the shaft and revolute force. The simulation of mechanism via ADAMS and an experiment is made to verify the design. The maximum stress is exposed in curved shaft and the worst working condition is the tilt condition. It proves the validity of tilting system that both mechanism and hydraulic system work well in the loading condition and unloading condition.

Co-simulation of multibody dynamics and discrete element method for hydraulic excavators

Multibody dynamics (MBD) simulation is a useful tool to analyse the kinematic function of multibody systems, while discrete element method (DEM) is widely used to simulate particle flows in various types of equipment at the individual particle scale and as an overall process. A combination of MBD and DEM methods, such as functional mock-up interface (FMI) based co-simulation, could capture both updated material behaviour and equipment behaviour and predict the equipment performance. In this work, MBD and FMI co-simulations are based on the commercial software Dymola. MBD models have been developed for hydraulic excavator system. GPU-based DEM models have also been developed for excavator digging cycles. Finally, MBD-DEM FMI co-simulation results show that solid materials can significantly affect the movement of excavators. • MBD model for a simplified excavator is developed based on Dymola. • MBD dig cycles can be flexibly adjusted. • GPU-based DEM model is developed with dynamic computational domain. • MBD-DEM FMI co-simulation models have been developed. • Co-simulation results show the mutual effect of solid materials and excavator.

Functional evaluation of optimal index finger proximal interphalangeal joint fusion angle using a simulated joint arthrodesis

This study aims at qualitatively and quantitatively evaluating the effects of simulated index finger proximal interphalangeal (PIP) joint fusion angles on hand kinematic function and performance. Although arthrodesis of the index finger PIP joint is an effective medical procedure that produces a durable, pain-free, and stable joint, it permanently immobilizes the joint. Twenty healthy subjects performed basic functional hand activities with the index finger PIP joint unconstrained (UC) and constrained to selected angles under surveillance of a motion capture system. Our results indicate differences in perceived difficulty, time performance, and the functional ROM of the hand joints when the index finger PIP joint is UC and constrained to 0, 20, and 40 degrees of flexion. The mean total perceived difficulty scores for all 6 tasks were higher for the PIP at 0 degrees than for the UC condition (p < 0.001) and for the PIP at 40 degrees (p = 0.048). The functional ROM presented a smaller total number of hand joints affected by the PIP at 20 degrees (25 in total) than the PIP at 0 (31 in total) and 40 (27 in total) degrees during execution of all 6 tasks tested. Therefore, the decision on the appropriate index finger PIP angle for arthrodesis may be between 20 and 40 degrees, as globally for all 6 tasks tested, 0 degrees exhibited the worst results regarding perceived difficulty, performance time, and number of joints with affected ROM. Selecting the appropriate angle for arthrodesis should consider a more complete set of functional activities.

Prediction of male fertility using Ras-related proteins

Identifying effective biomarkers for the diagnosis of male fertility is crucial for improving animal production and treating male infertility in humans. Ras-related proteins (Rab) are associated with morphological and motion kinematic functions in spermatozoa. Moreover, Rab2A, a Rab protein, is a possible male fertility-related biomarker. The present study was designed to identify additional fertility-related biomarkers among the various Rab proteins. First, the expression of Rab proteins (Rab3A, 4, 5, 8A, 9, 14, 25, 27A, and 34A) from 31 duroc boar spermatozoa was measured before and after capacitation; correlation between Rab protein expression and litter size was evaluated by statistical analysis. The results showed that the expression of Rab3A, 4, 5, 8A, 9, and 25 before capacitation and Rab3A, 4, 5, 8A, 9, and 14 after capacitation were negatively correlated with litter size. Moreover, depending on the cut-off values calculated by receiver operating curves, an increase in litter size was observed when evaluating the ability of the Rab proteins to forecast litter size. Therefore, we suggest that Rab proteins may be potential fertility-related biomarkers that could help select superior sires in the livestock industry.

Celestial holography on Kerr-Schild backgrounds

We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

Machine-learning-based video analysis of grasping behavior during recovery from cervical spinal cord injury

Comprehensive characterizations of hand grasping behaviors after cervical spinal cord injuries are fundamental for developing rehabilitation strategies to promote recovery in spinal-cord-injured primates. We used the machine-learning-based video analysis software, DeepLabCut, to sensitively quantify kinematic aspects of grasping behavioral deficits in squirrel monkeys with C5-level spinal cord injuries. Three squirrel monkeys were trained to grasp sugar pellets from wells of varying depths before and after a left unilateral lesion of the cervical dorsal column. Using DeepLabCut, we identified post-lesion deficits in kinematic grasping behavior that included changes in digit orientation, increased variance in vertical and horizontal digit movement, and longer time to complete the task. While video-based analyses of grasping behavior demonstrated deficits in fine-scale digit function that persisted through at least 14 weeks post-injury, traditional end-point behavioral analyses showed a recovery of global hand function as evidenced by recovery of the proportion of successful retrievals by approximately 14 weeks post-injury. The combination of traditional end-point and video-based kinematic analyses provides a more comprehensive characterization of grasping behavior and highlights that global grasping performance may recover despite persistent fine-scale kinematic deficits in digit function. Machine-learning-based video analysis of kinematic digit function, in conjunction with traditional end-point behavioral analyses of grasping behavior, provide sensitive and specific indices for monitoring recovery of fine-grained hand sensorimotor behavior after spinal cord injury that can aid future studies that seek to develop targeted therapeutic interventions for improving behavioral outcomes.

Kinematic Graph for Motion Planning of Robotic Manipulators

We introduce a kinematic graph in this article. A kinematic graph results from structuring the data obtained from the sampling method for sampling-based motion planning algorithms in robotics with the motivation to adapt the method to the positioning problem of robotic manipulators. The term kinematic graph emphasises the fact that any path computed by sampling-based motion planning algorithms using a kinematic graph is guaranteed to correspond to a feasible motion for the positioning of the robotic manipulator. We propose methods to combine the information from the configuration and task spaces of the robotic manipulators to cluster the samples. The kinematic graph is the result of this systematic clustering and a tremendous reduction in the size of the problem. Hence, using a kinematic graph, it is possible to effectively employ sampling-based motion planning algorithms for robotic manipulators, where the problem is defined in higher dimensions than those for which these algorithms were developed. Other barriers that hindered adequate utilisation of such algorithms for robotic manipulators with articulated arms, such as the non-injective surjection of the forward kinematic function, are also addressed in the structure of the kinematic graph.

On Extracting Digitized Spiral Dynamics' Representations: A Study on Transfer Learning for Early Alzheimer's Detection.

This work proposes a decision-aid tool for detecting Alzheimer’s disease (AD) at an early stage, based on the Archimedes spiral, executed on a Wacom digitizer. Our work assesses the potential of the task as a dynamic gesture and defines the most pertinent methodology for exploiting transfer learning to compensate for sparse data. We embed directly in spiral trajectory images, kinematic time functions. With transfer learning, we perform automatic feature extraction on such images. Experiments on 30 AD patients and 45 healthy controls (HC) show that the extracted features allow a significant improvement in sensitivity and accuracy, compared to raw images. We study at which level of the deep network features have the highest discriminant capabilities. Results show that intermediate-level features are the best for our specific task. Decision fusion of experts trained on such descriptors outperforms low-level fusion of hybrid images. When fusing decisions of classifiers trained on the best features, from pressure, altitude, and velocity images, we obtain 84% of sensitivity and 81.5% of accuracy, achieving an absolute improvement of 22% in sensitivity and 7% in accuracy. We demonstrate the potential of the spiral task for AD detection and give a complete methodology based on off-the-shelf features.

Joint-Angle Adaptive Coordination Control of a Serial-Parallel Lower Limb Rehabilitation Exoskeleton

A serial–parallel lower limb rehabilitation exoskeleton can achieve a kinematic function similar to that of the human lower limb. Based on this bionic structure, joint-angle coordination is needed for model-based control. Because the kinematics of the parallel mechanism is difficult to solve, real-time attitude control of the task space cannot be realized. Moreover, owing to structural errors and parameter uncertainty, accurate modeling cannot be realized, which causes difficulties in system control. Therefore, based on existing modeling methods, adaptive control of a serial–parallel lower limb rehabilitation exoskeleton is proposed. The sensor of the parallel mechanism can realize accurate perception of the attitude, and the controller is designed to solve the control problem of the task space of the parallel component. A radial basis function neural network adaptive controller is used to compensate for the uncertainty and external disturbance of the model. Experiments were conducted to verify the effectiveness of the dynamic modeling and control system.

Influence Analysis of Geometric Error and Compensation Method for Four-Axis Machining Tools with Two Rotary Axes

Four-axis machine tools with two rotary axes are widely used in the machining of complex parts. However, due to an irregular kinematic relationship and non-linear kinematic function with geometric error, it is difficult to analyze the influence the geometry error of each axis has and to compensate for such a geometry error. In this study, an influence analysis method of geometric error based on the homogeneous coordinate transformation matrix and a compensation method was developed, using the Newton iterative method. Geometric errors are characterized by a homogeneous coordinate transformation matrix in the proposed method, and an error matrix is integrated into the kinematic model of the four-axis machine tool as a means of studying the influence the geometric error of each axis has on the tool path. Based on the kinematic model of the four-axis machine tool considering the geometric error, a comprehensive geometric error compensation calculation model based on the Newton iteration was then constructed for calculating the tool path as a means of compensating for the geometric error. Ultimately, the four-axis machine tool with a curve tool path for an off-axis optical lens was chosen for verification of the proposed method. The results showed that the proposed method can significantly improve the machining accuracy.