Direct Kinematic Model Research Articles

Kinematic Analysis of Planar Parallel Mechanism

The paper deals with kinematic model of parallel mechanism equipped with elastic members. The main aim is to determine the workspace of particular point of the mechanism in order to designing of whole mechanism for the future. Whole mechanisms should consist of several same segments which creates concept of serial mechanism. Since there is investigated parallel mechanism, at first has to be solved inverse kinematic model in order to obtain generalized variables, which are necessary for direct kinematic model. In the paper Jacobian matrix is derived for investigated mechanism. Then the algorithm for inverse kinematic model is described. The inverse kinematic model uses damped least squares method which appears as suitable method for our purposes. The results of inverse kinematic solution is consequently used for direct kinematic model, which is described by homogeneous transformation matrices. The planar parallel mechanism is simulated in software Matlab and the results are expressed in the graphs as well as our approach is discussed in the conclusion.

Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms

Compliant mechanisms are of great interest in precision engineering. In this paper, we propose a higher-order continuation method to help their rigid-body kinematic design. The method helps to investigate the choice of a mechanism configuration through the whole exploration of the workspace, and eases the kinematic analysis to avoid, or take advantage of, the vicinity of kinematic singularities. Such approach is relevant for planar and quasi-planar mechanisms that can be obtained with micro-manufacturing processes adapted to precision applications. The higher-order continuation method allows for a direct and accurate plotting of the input–output relationship of any mechanism by considering only its geometrical closed-loop equations, i.e. without the complex derivation of any analytical model. We show that these plots, called bifurcation diagrams, reveal essential information such as the joint velocity profile and the presence of singular configurations. Moreover, the continuous and accurate computation of the mechanism configuration in the vicinity of singularities provides detailed information about the kinematic behavior of the mechanism in its extreme positions. For the design of compliant mechanisms, the designer can advantageously use the bifurcation diagrams to evaluate the relevance of the selected mechanism, then to identify a configuration in order to obtain desired kinematic properties without the derivation of the inverse kinematic model (IKM) or the direct kinematic model (DKM). The method is exemplified with a 3 universal-joint and 3 spherical-joint mechanism (3-US), the IKM and DKM of which cannot be derived analytically. The latter has a large workspace and special kinematic behaviors consisting of a screw-like motion and a platform gyration, which have not been studied before and could lead to novel compliant devices.

Effects of hip joint centre mislocation on gait kinematics of children with cerebral palsy calculated using patient-specific direct and inverse kinematic models

Joint kinematics can be calculated by Direct Kinematics (DK), which is used in most clinical gait laboratories, or Inverse Kinematics (IK), which is mainly used for musculoskeletal research. In both approaches, joint centre locations are required to compute joint angles. The hip joint centre (HJC) in DK models can be estimated using predictive or functional methods, while in IK models can be obtained by scaling generic models. The aim of the current study was to systematically investigate the impact of HJC location errors on lower limb joint kinematics of a clinical population using DK and IK approaches. Subject-specific kinematic models of eight children with cerebral palsy were built from magnetic resonance images and used as reference models. HJC was then perturbed in 6mm steps within a 60mm cubic grid, and kinematic waveforms were calculated for the reference and perturbed models. HJC perturbations affected only hip and knee joint kinematics in a DK framework, but all joint angles were affected when using IK. In the DK model, joint constraints increased the sensitivity of joint range-of-motion to HJC location errors. Mean joint angle offsets larger than 5° were observed for both approaches (DK and IK), which were larger than previously reported for healthy adults. In the absence of medical images to identify the HJC, predictive or functional methods with small errors in anterior-posterior and medial-lateral directions and scaling procedures minimizing HJC location errors in the anterior-posterior direction should be chosen to minimize the impact on joint kinematics.

A unified dynamic algorithm for wheeled multibody systems with passive joints and nonholonomic constraints

This paper presents a systematic approach to develop a generalized symbolic/numerical dynamic algorithm for modeling and simulation of multibody systems with branches and wheels. The proposed dynamic algorithm includes the direct kinematic and inverse dynamic models of the wheeled systems with prismatic/revolute as well as actuated/passive degrees of freedom. Using the geometric configuration of the system through modified Denavit–Hartenberg convention, symbolic equations in general algorithmic form are developed for kinematic constraints associated with the wheel–ground contacts. The Newton–Euler equations are used to develop an algorithm for the inverse dynamic model of the multibody system. The complete algorithm is then used to solve the kinematics and dynamics of the system, and computes: (i) the kinematics of the external/internal passive degrees of freedom of the system, (ii) the Lagrange multipliers associated with the wheel–ground contacts, and (iii) the driving forces/torques of the actuated degrees of freedom. Some examples are solved with the help of the proposed algorithm, using MATLAB, to illustrate its implementation on different wheeled systems. These examples include a differential wheeled robot, a snake-like wheeled system, and a bicycle.

Prescribing joint co-ordinates during model preparation to improve inverse kinematic estimates of elbow joint angles

To appropriately use inverse kinematic (IK) modelling for the assessment of human motion, a musculoskeletal model must be prepared 1) to match participant segment lengths (scaling) and 2) to align the model׳s virtual markers positions with known, experimentally derived kinematic marker positions (marker registration). The purpose of this study was to investigate whether prescribing joint co-ordinates during the marker registration process (within the modelling framework OpenSim) will improve IK derived elbow kinematics during an overhead sporting task. To test this, the upper limb kinematics of eight cricket bowlers were recorded during two testing sessions, with a different tester each session. The bowling trials were IK modelled twice: once with an upper limb musculoskeletal model prepared with prescribed participant specific co-ordinates during marker registration – MRPC – and once with the same model prepared without prescribed co-ordinates – MR; and by an established direct kinematic (DK) upper limb model. Whilst both skeletal model preparations had strong inter-tester repeatability (MR: Statistical Parametric Mapping (SPM1D)=0% different; MRPC: SPM1D=0% different), when compared with DK model elbow FE waveform estimates, IK estimates using the MRPC model (RMSD=5.2±2.0°, SPM1D=68% different) were in closer agreement than the estimates from the MR model (RMSD=44.5±18.5°, SPM1D=100% different). Results show that prescribing participant specific joint co-ordinates during the marker registration phase of model preparation increases the accuracy and repeatability of IK solutions when modelling overhead sporting tasks in OpenSim.

Method for six-legged robot stepping on obstacles by indirect force estimation

Adaptive gaits for legged robots often requires force sensors installed on foot-tips, however impact, temperature or humidity can affect or even damage those sensors. Efforts have been made to realize indirect force estimation on the legged robots using leg structures based on planar mechanisms. Robot Octopus III is a six-legged robot using spatial parallel mechanism(UP-2UPS) legs. This paper proposed a novel method to realize indirect force estimation on walking robot based on a spatial parallel mechanism. The direct kinematics model and the inverse kinematics model are established. The force Jacobian matrix is derived based on the kinematics model. Thus, the indirect force estimation model is established. Then, the relation between the output torques of the three motors installed on one leg to the external force exerted on the foot tip is described. Furthermore, an adaptive tripod static gait is designed. The robot alters its leg trajectory to step on obstacles by using the proposed adaptive gait. Both the indirect force estimation model and the adaptive gait are implemented and optimized in a real time control system. An experiment is carried out to validate the indirect force estimation model. The adaptive gait is tested in another experiment. Experiment results show that the robot can successfully step on a 0.2 m-high obstacle. This paper proposes a novel method to overcome obstacles for the six-legged robot using spatial parallel mechanism legs and to avoid installing the electric force sensors in harsh environment of the robot’s foot tips.

Joint kinematic calculation based on clinical direct kinematic versus inverse kinematic gait models

Most clinical gait laboratories use the conventional gait analysis model. This model uses a computational method called Direct Kinematics (DK) to calculate joint kinematics. In contrast, musculoskeletal modelling approaches use Inverse Kinematics (IK) to obtain joint angles. IK allows additional analysis (e.g. muscle-tendon length estimates), which may provide valuable information for clinical decision-making in people with movement disorders.The twofold aims of the current study were: (1) to compare joint kinematics obtained by a clinical DK model (Vicon Plug-in-Gait) with those produced by a widely used IK model (available with the OpenSim distribution), and (2) to evaluate the difference in joint kinematics that can be solely attributed to the different computational methods (DK versus IK), anatomical models and marker sets by using MRI based models.Eight children with cerebral palsy were recruited and presented for gait and MRI data collection sessions. Differences in joint kinematics up to 13° were found between the Plug-in-Gait and the gait 2392 OpenSim model. The majority of these differences (94.4%) were attributed to differences in the anatomical models, which included different anatomical segment frames and joint constraints. Different computational methods (DK versus IK) were responsible for only 2.7% of the differences. We recommend using the same anatomical model for kinematic and musculoskeletal analysis to ensure consistency between the obtained joint angles and musculoskeletal estimates.

Calibration of a parallel mechanism in a serial-parallel polishing machine tool based on genetic algorithm

The calibration is very important to improve the accuracy of the parallel mechanism. This paper proposed a new calibration approach for the parallel mechanism based on the direct kinematics model and the genetic algorithm. The proposed calibration approach avoids the measurement of the absolute position/posture of the moving platform in the calibration. Firstly, the ideal kinematics model, as well as the kinematics model with errors, of the parallel mechanism in the hybrid machine tool is established. Due to the absence of an analytical solution to the direct kinematics, the Newton iterative method is used to provide a solution. Since the calibration of the parallel mechanism can be regarded as a discrete optimization problem of multiple designed variables, the genetic algorithm is specifically used to identify the parameters in the kinematics model. Finally, the calibration experiment is carried out to verify the effectiveness of the proposed method. According to the experimental results, the positioning error of the parallel mechanism is largely reduced from 0.083 to 0.018 mm.

Quaternion-Based Algorithm for Direct Kinematic Model of a Kawasaki FS10E Articulated Arm Robot

This article follows a detailed description of development and validation for the direct kinematic model of six degrees of freedom articulated arm robot - Kawasaki FS10E model. The development of the kinematic model is based on widely used Denavit-Hartenberg notation, but, after the initial parameter identification, the mathematical algorithm itself follows an approach that uses the quaternion number system, taking advantage of their efficiency in describing spatial rotation - providing a convenient mathematical notation for expressing rotations and orientations of objects in three-dimensional space. The proposed algorithm concludes with two quaternion-based relations that express both the position of robot tool center point (TCP) position and end-effector orientation with respect to robot base coordinate system using Denavit-Hartenberg parameters and joint values as input data. Furthermore, the developed direct kinematic model was validated using the programming and offline simulation software Kawasaki PC Roset.

Adaptive Robust Three-dimensional Trajectory Tracking for Actively Articulated Tracked Vehicles*

A new approach is proposed for an adaptive robust three-dimensional (3D) trajectory-tracking controller design. The controller is modeled for actively articulated tracked vehicles (AATVs). These vehicles have active sub-tracks, called flippers, linked to the ends of the main tracks, to extend the locomotion capabilities in hazardous environments, such as rescue scenarios. The proposed controller adapts the flippers configuration and simultaneously generates the track velocities, to allow the vehicle to autonomously follow a given feasible 3D path. The approach develops both a direct and differential kinematic model of the AATV for traversal task execution correlating the robot body motion to the flippers motion. The benefit of this approach is to allow the controller to flexibly manage all the degrees of freedom of the AATV as well as the steering. The differential kinematic model integrates a differential drive robot model, compensating the slippage between the vehicle tracks and the traversed terrain. The underlying feedback control law dynamically accounts for the kinematic singularities of the mechanical vehicle structure. The designed controller integrates a strategy selector too, which has the role of locally modifying the rail path of the flipper end points. This serves to reduce both the effort of the flipper servo motors and the traction force on the robot body, recognizing when the robot is moving on a horizontal plane surface. Several experiments have been performed, in both virtual and real scenarios, to validate the designed trajectory-tracking controller, while the AATV negotiates rubble, stairs, and complex terrain surfaces. Results are compared with both the performance of an alternative control strategy and the ability of skilled human operators, manually controlling the actively articulated components of the robot.

Cinemática inversa de robot serial utilizando algoritmo genético basado en MCDS

Los robots manipuladores seriales son herramientas eficaces para realizar tareas repetitivas y de precisión en la industria, siempre que se comprenda la cinemática involucrada en el posicionamiento y orientación del efector final. Este artículo presenta una metodología para resolver el problema cinemático inverso de un robot serial (Melfa RV-2A) utilizando un algoritmo genético (AG) a partir del modelo cinemático directo Screws (MCDS). Para esto, se obtienen los parámetros Screw que modelan el robot, se calcula el espacio de trabajo asociado y se diseña el AG contemplando una función multi-objetivo de alcance de posición y orientación en que se sitúa el efector final, con respecto a una coordenada y orientación de un punto objetivo establecido. La validación del AG se realiza según la aptitud, el tiempo de convergencia y la cantidad de generaciones usadas por la función para alcanzar el objetivo. Por tanto, la implementación de un AG basado en un MCDS es una herramienta prometedora que podría utilizarse para calcular la cinemática inversa de robots seriales. Esta novedosa implementación permite establecer por primera vez la exposición matricial de un sistema cinemático directo para obtener la solución cinemática inversa de un robot serial. En consecuencia, se demuestra que esta es una metodología factible y eficiente para solucionar la cinemática inversa de cualquier tipo de robot manipulador.

A Study of Calculation Method for Finger Joint Angular Displacement Based on the Finger Inverse Kinematics

A simple method for measuring and calculating the finger joint angular displacement was proposed to serve as the basis for designing dexterous hand and rehabilitation robot hand. The direct kinematics model and the inverse kinematics equation of the finger were established at the beginning of this paper. Then, the trajectory of the fingertip, from which the coordinates of the fingertip were extracted by using AutoCAD, was captured by camera. Finally, the trajectory coordinates of the fingertip were substituted into the inverse kinematics equations to solve the angular displacements of the proximal interphalangeal (PIP), distal interphalangeal (DIP) and metacarpophalangeal (MCP) joints. The calculating precision testing of the finger joint angular displacement needs to substitute the angular displacements calculated before into the direct kinematics equations of the finger to calculate the trajectory of the fingertip. Then, the average Euclidean distance between the calculated trajectory and the real trajectory was computed to test the calculating precision of the finger joint angular displacement. The average Euclidean distance of each fingers is less than 0.05mm, which proves the high calculating precision of the finger joint angular displacement and the efficiency of the method presented in this paper.

Comprehensive kinematic modeling and analysis of a coaxial helicopter’s swashplate mechanism

A comprehensive mathematical model of a coaxial helicopter’s swashplate mechanism is established, analyzed and verified in this paper. The mechanism widely used in helicopters to manipulate blade pitch angles is complex because of its configuration of multi closed-loop kinematic chains, especially for coaxial layout. First, geometrical method is used in determining the direct and inverse position kinematics. Based on that model, an approach of differentiation on spatial vectors is adopted to induce the relative velocity and acceleration matrices of every part of the system. The influence of rotors’ rotation is also considered in the modeling of velocity and acceleration kinematics to obtain a comprehensive model. The workspace and dexterity characteristics are analyzed in detail under the constraint of actuators’ inputs. After that, the complete direct kinematic model is simulated with consideration of control allocation and actuator dynamics. Finally, an integrated verification approach is designed based on experimental and simulative method to validate the established model. The work is concluded with an application prospect in future.

Design and Development of a Novel Coordinate Measuring Machine with 3-PUU Parallel Mechanism

A bran-new style coordinate measuring system with 3-PUU parallel mechanism and its advantages was proposed which could realize 3D measurement with only one linear grating and two precision guides. Firstly, measuring space with a 0.05mm error of structure parameter as target was explored based on 6 bars direct kinematics model, workspace and error model, and then the principle of maximum measuring space was presented to elaborate the relationship between measuring space and length of bar. Then in order to enlarge the scale of measuring space of Coordinate Measuring Machine (CMM), improve the measuring accuracy and flexibility of CMM, the key dimensions and positional parameters of CMM were optimization designed according to the direct kinematics model and the principle of maximum measuring space. Finally the deformation of key components was processed by Finite Element Method (FEM) according to the motion characteristics and parameters of the new CMM prototype, so that the affect of deformation to measuring accuracy can be controlled and decreased. Results are shown that the measuring space of CMM is 1100mm in x axis, 535mm in y axis, 426mm in z axis; deformation of beam is the main reason to influence the measuring accuracy and should be offset after calibration.

Kinematic, workspace and singularity analysis of a new parallel robot used in minimally invasive surgery

In the last ten years, due to development in robotic assisted surgery, the minimally invasive surgery has greatly changed. Until now, the vast majority of robots used in surgery, have serial structures. Due to the orientation parallel module, the structure is able to reduce the pressure exerted on the entrance point in the patient’s abdominal wall. The parallel robot can also handle both a laparoscope as well an active instrument for different surgical procedures. The advantage of this parallel structure is that the geometric model has been obtained through an analytical approach. The kinematic modelling of a new parallel architecture, the inverse and direct geometric model and the inverse and direct kinematic models for velocities and accelerations are being determined. The paper will demonstrate that with this parallel structure, one can obtain the necessary workspace required for a minimally invasive operation. The robot workspace was generated using the inverse geometric model. An indepth study of different types of singularity is performed, allowing the development of safe control algorithms of the experimental model. Some kinematic simulation results and the experimental model of the robot are presented in the paper.

Kinematic Analysis of Humanoid Robot Hand

The paper deals with kinematic analysis of humanoid robot hand. The first of all the biological aspects of humanoid hand are discussed. Then the kinematic configuration of humanoid robot hand with 23 DOF is designed. This configuration should be able to do operations like grasping, holding or squeezing. In the paper the direct kinematic model is established using homogeneous transformation matrices. Consequently the workspace of particular finger can be obtain by suitable plotting algorithm in Matlab.

Kinematic calibration of a five-bar planar parallel robot using all working modes

We present a simple low-cost calibration procedure that improves the planar positioning accuracy of a double-arm SCARA robot to levels difficult or impossible to achieve using an equivalent serial robot. Measurements are based on the use of five custom designed magnetic tooling balls fixed to the periphery of a detachable working plate. Three of these tooling balls define the world reference frame of the robot, and the positions of the centers of all balls are measured on a CMM. A special magnetic cup end-effector is used. Measurements are taken by manually positioning the end-effector over each of the tooling balls, with each of the maximum of four possible robot configurations. Each of these measurements is repeatable to within±0.015 mm. The robot calibration model includes all 12 kinematic parameters, and the calibration method used is based on the linearization of the direct kinematics model in each calibration configuration. The optimal number and location of the tooling balls is obtained by studying the observability index. Finally, an experimental validation at 14 additional tooling balls shows that the maximum position error with respect to the world frame is reduced to 0.080 mm within the entire robot's workspace of 600 mm×600 mm.

Analysis and evaluation of objective functions in kinematic calibration of parallel mechanisms

This paper analyses different objective functions for the parameter identification of parallel mechanisms and studies the influence in the position and orientation errors to improve their accuracy. A new objective function considering deviation terms is presented. This function is compared with other widely used functions and the advantages and disadvantages of each function are presented. The geometric parameter identification is performed by external calibration by means of the direct kinematic model. First, the objective functions are defined considering error position, error orientation and deviations in measurement. These functions compare the measured and calculated moving platform coordinates in order to obtain the identified model parameters that minimize this difference. The measured coordinates are obtained by measuring three sphere centres, fixed to the moving platform of a parallel mechanism, and the computed coordinates are given by the kinematic model. Second, the model is solved by the Levenberg–Marquardt algorithm for a number of identification positions. Finally, the calibration is verified in test positions. The results obtained show that the consideration of the deviations in measurement in the objective function with respect to classical approaches allows us to better identify those kinematic parameters corresponding with passive joints that cannot be measured. These findings confirm that a suitable objective function can improve the mechanism accuracy by more than one order of magnitude in both position and orientation errors.

Human Gait Feature Extraction Including a Kinematic Analysis toward Robotic Power Assistance

The present work proposes a method for human gait and kinematic analysis. Gait analysis consists of the determination of hip, knee and ankle positions through video analysis. Gait kinematic for the thigh and knee is then generated from this data. Evaluations of the gait analysis method indicate an acceptable performance of 86.66% for hip and knee position estimation, and comparable findings with other reported works for gait kinematic. A coordinate systems assignment is performed according to the DH algorithm and a direct kinematic model of the legs is obtained. The legs' angles obtained from the video analysis are applied to the kinematic model in order to revise the application of this model to robotic legs in a power assisted system.

Direct Kinematic Modeling of the Upper Limb During Trunk-Assisted Reaching

The study proposes a rigid-body biomechanical model of the trunk and whole upper limb including scapula and the test of this model with a kinematic method using a six-dimensional (6-D) electromagnetic motion capture (mocap) device. Large unconstrained natural trunk-assisted reaching movements were recorded in 7 healthy subjects. The 3-D positions of anatomical landmarks were measured and then compared to their estimation given by the biomechanical chain fed with joint angles (the direct kinematics). Thus, the prediction errors was attributed to the different joints and to the different simplifications introduced in the model. Large (approx. 4 cm) end-point prediction errors at the level of the hand were reduced (to approx. 2 cm) if translations of the scapula were taken into account. As a whole, the 6-D mocap seems to give accurate results, except for prono-supination. The direct kinematic model could be used as a virtual mannequin for other applications, such as computer animation or clinical and ergonomical evaluations.