Academic literature on the topic 'Denavit-Hartenberg'

The Lie group Denavit–Hartenberg method and application in the parallel hexapod robot are researched. The hexapod robot and the ground form opened and closed loop alternately; the complete kinematics equation cannot be derived by Denavit–Hartenberg method with a trigonometric function type. The complete kinematics model of the hexapod robot is constructed with the improved Denavit–Hartenberg method. The numerical solving strategy is schemed. The simulation results provide the positive and athwart kinematics response relation during the lift and forward patterns in space. The research shows that the complete kinematics model can be constructed by the Lie group Denavit–Hartenberg method; the numerical calculation method can solve the pose–attitude response correctly.

Drilling robot is a piece of large rock drilling equipment that integrates mechanical, electrical, and hydraulic technique, and it is a significant device for drilling and blasting. The drilling robot arm is the core component of the robot. To get intuitive and accurate modeling method to overcome the problem of the classic Denavit–Hartenberg method, for instance, the model mismatches the entity. The coordinate system fixed on the entity of Denavit–Hartenberg notation that is named coordinate-fixed Denavit–Hartenberg is creatively presented. The coordinate-fixed Denavit–Hartenberg method not only improves the accuracy and operability of kinematic analysis but also solves the workspace of drilling robot arm effectively. The drilling robot from an intelligent technology company in China is taken as the research example in this article. The homogeneous coordinate transformation matrix of each link rod is established through reasonably simplifying drilling robot arm as a multijoint structure. The coordinate-fixed Denavit–Hartenberg method is utilized for the first time in determining and verifying the kinematics equation of drilling robot arm. The kinematics equation is employed to obtain the effective workspace of drilling robot arm. The analysis results demonstrate that the design of drilling robot arm reaches the need of workspace in the actual structure as well as meets the functional requirements of drilling robot.

This work focuses primarily on the D-H method, as one of the most important methods used in the process of designing robotic structures. In the introduction, the history of the D-H method and its general use is briefly mentioned. In the following section, the algorithm for applying D-H in the form of mathematical formalism is explained. In this part, the individual steps of creating transformational relationships are explained in more detail. The next chapters deal in more detail with individual application types within service robotics. The first type deals with the application deployment of the mobile robotic platform, the second deals with the mobile humanoid robotic structure, the other deals with the fourlegged robotic mechanism and the last type with the application of the robotic arm.

One of the most popular mathematical tools in the fields of robotics and mechanisms is the Denavit-Hartenberg (DH) notation (Denavit and Hartenberg, 1955, J. Appl. Mech., 77, pp. 215–221). It is valid only for mechanisms containing prismatic, revolute, helical, and cylindrical pairs, but cannot be applied to spherical pairs. This paper presents an extended DH notation that includes spherical pairs, consequently allowing the required independent parameters of any spatial binary mechanism to be listed for purposes of analysis and synthesis. Further, the interference-free region with maximum ball-retention capability of a socket in a spherical pair can be determined analytically. Extended DH notation can systematically model arbitrary binary mechanisms with spherical pairs, simplifying their design and study.

This paper presents a method to build the forward kinematics model of a bucket excavator’s digging equipment. The applied method is the one used for the industrial robots’ mechanisms and uses Denavit-Hartenberg convention.

<p class="MDPI17abstract"><span lang="EN-US">The paper presents a modified Denavit-Hartenberg coordinate system resulted from joint application of graph theory and the Denavit-Hartenberg coordinate system, which was developed to describe the kinematics of robot actuators with a linear open kinematic chain. It allows forming mathematical models of actuating mechanisms for the robots with tree-like kinematic structures. The work introduces the concept of primary and auxiliary coordinate systems. It considers an example of making the links’ reachability matrix and reachability graph for the tree-like actuating mechanism of a robotic mannequin. The use efficiency of the proposed modified Denavit-Hartenberg coordinate system is illustrated by the examples giving the mathematical description of the kinematics and dynamics of specific robots’ tree-like actuating mechanisms discussed in the previously published papers. It is shown that the proposed coordinate system can also be successfully applied to describe the actuating mechanisms of robots with a linear open kinematic chain, which is a particular case of the tree-like kinematic structure. The absence of branching joints in it does not require introducing auxiliary coordinate systems and the parameters f(i) and ns(i) are necessary only for the formal notation of equations, which have similar forms for the tree-like and linear chains. In this case, the modified and traditional coordinate systems coincide.</span></p>

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-27T14:34:02Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Carlos Gomides da Costa - 2014.pdf: 5662268 bytes, checksum: 9c271f8544a1ec02f89c341d68f33801 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-28T12:36:28Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Carlos Gomides da Costa - 2014.pdf: 5662268 bytes, checksum: 9c271f8544a1ec02f89c341d68f33801 (MD5)<br>Made available in DSpace on 2015-01-28T12:36:28Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Carlos Gomides da Costa - 2014.pdf: 5662268 bytes, checksum: 9c271f8544a1ec02f89c341d68f33801 (MD5) Previous issue date: 2014-08-08<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This work have as the main objective present one a different way to teach the subject matrix multiplication, a way in a ludic form, applied, that can transform the teaching more pleasureable and motivate for the high scholl students, because for many this issue has no practical applications, which for many reasons is the lack of interest in learning such content. The tool used to attract as students so as teachers was the utilization of Kit LEGO® Mindstorms NXT 2.0 for the construction of the robotic arm, or robotic manipulator, that which for this propose, has three rotational joints. The LEGO kit was choosen due its easy interaction with children and adolescents, and to encourage the construction of knowledge stimulating the solution of problems that may arise during the process of building robotic arm.The application of content takes place in obtaining the four parameters Denavit-Hartenberg and those obtained after the placement of reference systems, where three of these parameters are constants obtained by measurement at robotic arm and the fourth parameter is variable dependent on the intended movement or the final position which is to be determined.<br>O presente trabalho tem como principal objetivo apresentar mais uma opção de ensinar o assunto multiplicação de matrizes, de uma forma mais lúdica, aplicada, que pode tornar o ensino mais prazeroso e atrativo para alunos do ensino médio, pois para muitos esse assunto não tem aplicações práticas, o que para outros é motivo da falta de interesse em aprender tal conteúdo. A ferramenta apresentada com o intuito de atrair tanto alunos quanto professores, foi o Kit LEGO® Mindstorms NXT 2.0, que possibilitou a construção do braço robótico ou manipulador robótico, que nesse trabalho foi apresentado com três juntas do tipo rotacionais. A escolha desse Kit LEGO® é justificada pela sua facilidade de interação com crianças e adolescentes, além de estimular a construção do aprendizado pois, estimula a solução de problemas que possam aparecer durante o processo de construção do braço robótico. A aplicação do conteúdo se dá na obtenção dos quatro parâmetros de Denavit-Hartenberg que são obtidos após a colocação dos sistemas de referência, onde três desses parâmetros são definidos a partir de medições feitas no braço robótico e o quarto parâmetro é variável dependente do movimento pretendido ou a posição final que se queira determinar.

La modélisation et la simulation numérique sont des outils fondamentaux pour la conception et le développement de nouveaux véhicules. Les travaux de cette thèse portent sur la modélisation et la simulation d'un véhicule innovant, étroit et inclinable, en appliquant une description systématique et générique du véhicule considéré comme un robot dont la base est mobile et les roues sont les organes terminaux. Le système d'inclinaison motorisé entraîne une cinématique complexe et comporte des chaines fermées. Le but du travail est de construire un modèle physique précis, au contraire des modèles simplifiés de type bicyclette ou quart de véhicule utilisés habituellement pour l'étude de la commande des véhicules. L'approche procède à la description de l'architecture mécanique du véhicule, le considérant comme un système multi-corps poly-articulés, s'appuyant sur le formalisme de la robotique et précisément sur la représentation géométrique de Denavit-Hartenberg modifié. Cette approche permet de calculer automatiquement les expressions symboliques des modèles géométriques, cinématiques et dynamiques des structures simples et arborescentes. Les modèles qui en résultent comportent un nombre minimum d'opérations par la mise à profit du calcul symbolique itératif et des techniques de simplification de modèles propres à la robotique. Ces techniques sont implémentées dans le logiciel de calcul symbolique SYMORO+. Le modèle dynamique est calculé d'une manière récursive à l'aide de l'algorithme de Newton-Euler. La simulation dynamique utilise un simulateur édité sous Matlab/Simulink qui intègre le modèle dynamique direct calculé automatiquement à partir du modèle inverse. Des simulations réalisées sur des modèles de complexité croissante, pour des scénarios de freinage ou d'accélération, en ligne droite ou en virage, valident la méthodologie de modélisation mécanique proposée.

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009.<br>The input orientation of the excavators in use today usually comprises two joysticks that control the actuator links individually. In order to perform an excavation task, several different combinations of joystick inputs are required, placing high psychomotor demands on the operator. In training an operator this creates a steep learning curve, with a lengthy training time and a reasonable amount of experience being required to perform an excavation task skilfully. In this master’s thesis a haptic1 device was developed, resolving input ergonomics and creating a single input device capable of providing feedback to the operator. The design and construction of the haptic device, with the related control scheme, is presented and discussed. The control scheme combines position and rate control, and relates all the actuator joint positions to a single end-effector point. The control and ergonomic aspects of the haptic device were tested and compared to the traditional two joystick control setup by means of the implementation of a virtual excavator simulator. The simulation was developed in MATLAB, and virtual excavator displayed in an openGL window. The objective of this study was to evaluate the human factors related to the input orientation. Ten inexperienced test subjects were recruited to perform four sets of tests, where each test required a different level of operator skill. The results indicated that, on average, the test subjects had an increased level of performance after training on the haptic device. These results strongly support the hypothesis that haptic control simplifies the operational tasks required for operating an excavator. 1The word haptic means of, or relating to, the sense of touch, or tactile

The present thesis deals with the study of vision techniques for the detection of human pose based on the analysis of a single image, as well as the tracking of these poses along a sequence of images. It is proposed to model the human pose by four kinematic chains that model the four articulated extremities. These kinematic chains and head remain attached to the body. The four kinematic chains are composed by three keypoints. Therefore, the model initially has a total of $14$ parts. In this thesis it is proposed to modify the technique called Deformable Parts Model (DPM), adding the depth channel. Initially, the DPM model was defined over three RGB channel images. While in this thesis it is proposed to work on images of four RGBD channels, so the proposed extension is called 4D-DPM. The experiments performed with 4D-DPM demonstrate an improvement in the accuracy of pose detection with respect to the initial DPM model, at the cost of increasing its computational cost when treating an additional channel. On the other hand, it is defined to reduce the previous computational cost by simplifying the model that defines the human pose. The idea is to reduce the number of variables to be detected with the 4D-DPM model, so that the suppressed variables can be calculated from the detected variables using inverse kinematics models based on dual quaternions. In addition, it is proposed to use a particle filter models to continue improving the accuracy of detection of human poses along a sequence of images. Considering the problem of detection and monitoring of human body pose along a video sequence, this thesis proposes the use of the following method. 1. Camara calibration. RGBD image processing. Subtraction of the image background with the MSER method. 2. 4D-DPM: method used to detect the keypoints (variables of the pose model) within an image. 3. Particle filters: this type of filter is designed to track the keypoints over time and correct the data obtained by the sensor. 4. Inverse kinematic modeling: the control of kinematic chains is performed with the help of dual cuaternions in order to obtain the complete pose model of the human body. The overall contribution of this thesis is the proposal of the previous method that, combining the previous methods, is able to improve the accuracy in the detection and the follow up of the human body pose in a video sequence, also reducing its computational cost . This is possible due to the combination of the 4D-DPM method with the use of inverse kinematics techniques. The original DPM method should detect $14$ point of interest on an RGB image to estimate the human pose. However, the proposed method, where a point of interest for each limb is removed, must detect $10$ point of interest on an RGBD image. Subsequently, the eliminated $4$ point of interest are calculated by using inverse kinematics methods from the calculated $10$ point of interest. To solve the problem of inverse kinematics a dual quaternions methods is proposed for each of the $4$ kinematic chains that model the extremities of the skeleton of the human body. The particle filter is applied over the time sequence of the 10 points of interest of the posture model detected through the 4D-DPM method. To design these particle filters it is proposed to add the following restrictions to weight the particles generated: 1. Restrictions on joint limits. 2. Softness restrictions. 3. Collision detection. 4. Projection of poly-spheres<br>La presente tesis trata sobre el estudio de técnicas de visión para la detección de la postura del esqueleto del cuerpo humano basada en el análisis de una sola imagen, además del seguimiento de estas posturas a lo largo de una secuencia de imágenes. Se propone modelar la postura del esqueleto cuerpo humano mediante cuatro cadenas cinemáticas que modelan las cuatro extremidades articuladas. Estas cadenas cinemáticas y la cabeza permanecen unidas al cuerpo. Las cuatro cadenas cinemáticas se componen de tres puntos de interés. Por lo tanto, el modelo inicialmente dispone de un total de 14 puntos de interés. En esta tesis se propone modificar la técnica denominada Deformable Parts Model (DPM), añadiendo el canal de profundidad denominado ``Depth''. Inicialmente el modelo DPM se definió sobre imágenes de tres canales RGB. Mientras que en esta tesis se propone trabajar sobre imágenes de cuatro canales RGBD, por ello a la ampliación propuesta se le denomina 4D-DPM. Por otra parte, se propone reducir el coste computacional anterior simplificando el modelo que define la postura del cuerpo humano. La idea es reducir el número de variables a detectar con el modelo 4D-DPM, de tal manera que las variables suprimidas se puedan calcular a partir de las variables detectadas, utilizando modelos de cinemática inversa basados en cuaterniones duales. Los experimentos realizados demuestran que la combinación de estas dos técnicas permite, reduciendo el coste computacional del método original DPM, mejorar la precisión de la detección de postura debido a la información extra del canal de profundidad. Adicionalmente, se propone utilizar modelos de filtros de partículas para continuar mejorando la precisión de la detección de las posturas humanas a lo largo de una secuencia de imágenes. Atendiendo al problema de detección y seguimiento de las postura del esqueleto del cuerpo humano a lo largo de una secuencia de vídeo, esta tesis propone el uso del siguiente método. 1. Calibración de cámaras. Procesamiento de imágenes RGBD. Sustracción del fondo de la imagen con el método MSER. 2. 4D-DPM: método utilizado para detectar los puntos de interés (variables del modelo de postura) dentro de una imagen. 3. Filtros de partículas: se diseña este tipo de filtros para realizar el seguimiento de los puntos de interés a lo largo del tiempo y corregir los datos obtenidos por el sensor. 4. Modelado cinemático inverso: se realiza el control de cadenas cinemáticas con la ayuda de cuaterniones duales con el fin de obtener el modelo completo de la postura del esqueleto del cuerpo humano. La contribución global de esta tesis es la propuesta del método anterior que, combinando los métodos anteriores, es capaz de mejorar la precisión en la detección y el seguimiento de la postura del esqueleto del cuerpo humano en una secuencia de vídeo, reduciendo además su coste computacional. El método original DPM debe detectar 14 puntos de interés sobre una imagen RGB para estimar la postura de un cuerpo humano. Sin embargo, el método propuesto debe detectar 10 puntos de interés sobre una imagen RGBD. Posteriormente, los 4 puntos de interés eliminados se calculan mediante la utilización de métodos de cinemática inversa a partir de los 10 puntos de interés calculados. Para resolver el problema de la cinemática inversa se propone utilizar cuaterniones duales para cada una de las 4 cadenas cinemáticas que modelan las extremidades del esqueleto del cuerpo humano. El filtro de partículas se aplica sobre la secuencia temporal de los 10 puntos de interés del modelo de postura detectados a través del método 4D-DPM. Para diseñar estos filtros de partículas se propone añadir las siguientes restricciones, explicadas en la memoria, para ponderar las partículas generadas: 1. Restricciones en los límites de articulaciones. 2. Restricciones de suavidad. 3. Detección de colisiones. 4. Proyección de las poli-esferas.<br>La present tesi tracta sobre l'estudi de tècniques de visió per a la detecció de la postura de l'esquelet del cos humà basada en l'anàlisi d'una sola imatge, a més del seguiment d'estes postures al llarg d'una seqüència d'imatges. Es proposa modelar la postura de l'esquelet del cos humà per mitjà de quatre cadenes cinemàtiques que modelen les quatre extremitats articulades. Estes cadenes cinemàtiques i el cap romanen unides al cos. Les quatre cadenes cinemàtiques es componen de tres punts d'interés. Per tant, el model inicialment disposa d'un total de $14$ punts d'interés. En esta tesi es proposa modificar la tècnica denominada Deformable Parts Model (DPM) , afegint el canal de profunditat denominat ``Depth''. Inicialment el model DPM es va definir sobre imatges de tres canals RGB. Mentres que en esta tesi es proposa treballar sobre imatges de quatre canals RGBD, per això a l'ampliació proposada se la denomina 4D-DPM. D'altra banda, es proposa reduir el cost computacional anterior simplificant el model que definix la postura del cos humà. La idea és reduir el nombre de variables a detectar amb el model 4D-DPM, de tal manera que les variables suprimides es puguen calcular a partir de les variables detectades, utilitzant models de cinemàtica inversa basats en quaternions duals. Els experiments realitzats demostren que la combinació d'estes dos tècniques permet, reduint el cost computacional del mètode original DPM, millorar la precisió de la detecció de la postura degut a la informació extra del canal de profunditat. Addicionalment, es proposa utilitzar models de filtres de partícules per a continuar millorant la precisió de la detecció de les postures humanes al llarg d'una seqüència d'imatges. Atenent al problema de detecció i seguiment de les postura de l'esquelet del cos humà al llarg d'una seqüència de vídeo, esta tesi proposa l'ús del següent mètode. 1. Calibratge de càmeres. Processament d'imatges RGBD. Sostracció del fons de la imatge amb el mètode MSER. 2. 4D-DPM: mètode utilitzat per a detectar els punts d'interés (variables del model de postura) dins d'una imatge. 3. Filtres de partícules: es dissenya este tipus de filtres per a realitzar el seguiment dels punts d'interés al llarg del temps i corregir les dades obtingudes pel sensor. 4. Modelatge cinemàtic invers: es realitza el control de cadenes cinemàtiques amb l'ajuda de quaternions duals a fi d'obtindre el model complet de l'esquelet del cos humà. La contribució global d'esta tesi és la proposta del mètode anterior que, combinant els mètodes anteriors, és capaç de millorar la precisió en la detecció i el seguiment de la postura de l'esquelet del cos humà en una seqüència de vídeo, reduint a més el seu cost computacional. Açò és possible a causa de la combinació del mètode 4D-DPM amb la utilització de tècniques de cinemàtica inversa. El mètode original DPM ha de detectar 14 punts d'interés sobre una imatge RGB per a estimar la postura d'un cos humà. No obstant això, el mètode proposat ha de detectar 10 punts d'interés sobre una imatge RGBD. Posteriorment, els 4 punts d'interés eliminats es calculen per mitjà de la utilització de mètodes de cinemàtica inversa a partir dels 10 punts d'interés calculats. Per a resoldre el problema de la cinemàtica inversa es proposa utilitzar quaternions duals per a cada una de les 4 cadenes cinemàtiques que modelen les extremitats de l'esquelet del cos humà. El filtre de partícules s'aplica sobre la seqüència temporal dels 10 punts d'interés del model de postura detectats a través del mètode 4D-DPM. Per a dissenyar estos filtres de partícules es proposa afegir les següents restriccions per a ponderar les partícules generades: 1. Restriccions en els límits d'articulacions. 2. Restriccions de suavitat. 3. Detecció de col·lisions. 4. Projecció de les poli-esferes.<br>Martínez Bertí, E. (2017). SEGUIMIENTO DE PERSONAS APLICANDO RESTRICCIONES CINEMÁTICAS BASADAS EN MODELOS DE CUERPOS RÍGIDOS ARTICULADOS [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86159<br>TESIS

Notre travail porte sur la définition d'outils de conception préliminaire de mécanismes, capables de construire des solutions admissibles à partir d'un cahier des charges donné et de débuter le processus de conception (esquisse et dimensionnement approché des formes des pièces).<br /><br />Dans cette optique, nous proposons une méthode de conception adaptée à la classe des mécanismes de transmission de mouvement rotatif, à structure linéaire, à 1 degré de mobilité et à rapport constant. Le logiciel CASYMIR (Conception Assistée de SYstèmes Mécaniques de transmIssion en Rotation) a été développé pour illustrer cette démarche qui comporte 3 étapes :<br /><br />À l'étape de synthèse topologique, un algorithme créatif génère l'ensemble des mécanismes-solutions admissibles. Il est basé sur l'exploration combinatoire d'une base de mécanismes (engrenages, courroies, trains épicycloïdaux, accouplements, etc.) et sur des règles de conception permettant d'éliminer les combinaisons inadaptées. Les mécanismes-solutions sont classés par ordre de préférence grâce à une méthode multi-critères ou par un algorithme de logique floue.<br /><br />Pour le pré-calcul dimensionnel, nous proposons la notion de squelette de mécanisme, qui est une représentation filaire spatiale des arbre, des entraxes et des angles du mécanisme. On peut alors construire un modèle géométrique basé sur celui de Denavit-Hartenberg puis l'optimiser pour trouver la position et l'orientation des étages minimisant l'encombrement et vérifiant les conditions de fermeture du mécanisme.<br /><br />La dernière étape de synthèse dimensionnelle permet de calculer les dimensions principales du mécanisme en intégrant des contraintes à la fois géométriques (non interférence des pièces, continuité géométrique et cinématique) et technologiques (résistance des dentures d'engrenages, rapport de réduction, etc.) au sein d'un même problème d'optimisation.<br /><br />Enfin, l'étude d'un réducteur industriel permet de valider le logiciel et la démarche.

碩士<br>國立臺灣科技大學<br>材料科學與工程系<br>103<br>Industrial robot arms are the indispensable equipment that have been widely used in automatic situation. They substitute high amount of human force to execute high dangerous and repetitive work. Position accuracy is one of the important performance of robot arms. However, when a robot arm is under manufacturing or assembly process, there are several reasons that would cause imprecise manufacturing, set up errors, gear backlash, gear transmission error, transmission errors and compliance, etc. In this study, we propose a low cost and time saving method by using robot arm kinematics model to estimate the geometric link parameters of the robot arm. In the experiments, encoders and micrometer are used to measure the joint positions and the position displacements of the robot arm respectively. By using the links parameters calibration method proposed in this study, we calibrate the industrial six-axis robot arm’s links parameters and update the geometric parameters of the robot arm. Finally, position error experiments are conducted to verify the accuracy of this calibration method.

Robots moving about in complex environments must be capable of determining and performing difficult motion sequences to accomplish tasks. As the tasks become more complicated, robots with greater dexterity are required. An increase in the number of degrees of freedom and a desire for autonomy in uncertain environments with real-time requirements leaves much room for improvement in the current popular robot motion planning algorithms. In this thesis, state of the art robot motion planning techniques are surveyed. A solution to the general movers problem in the context of motion planning for robots is presented. The proposed robot motion planner solves the general movers problem using a sample-based tree planner combined with an incremental simulator. The robot motion planner is demonstrated both in simulation and the real world. Experiments are conducted and the results analyzed. Based on the results, methods for tuning the robot motion planner to improve the performance are proposed.

This book chapter deals with kinematic modeling of serial robot manipulators (open-chain multibody systems) with focus on forward as well as inverse kinematic model. At first, the chapter describes basic important definitions in the area of manipulators kinematics. Subsequently, the rigid body motion is presented and basic mathematical apparatus is introduced. Based on rigid body conventions, the forward kinematic model is established including one of the most used approaches in robot kinematics, namely the Denavit-Hartenberg convention. The last section of the chapter analyzes inverse kinematic modeling including analytical, geometrical, and numerical solutions. The chapter offers several examples of serial manipulators with its mathematical solution.

The Denavit-Hartenberg conventions model chains of bodies connected by joints. Originally they were applied to single-loop chains but are now almost universally applied to open-loop serial chains such as robotic manipulators. Unfortunately there are several popular variations of the notation: the original, the distal variant, and the proximal variant. These three cases are compared for their application to serial robots. The proximal variate is advanced as the most notationally transparent for the mechanical analysis of serial manipulators.

Abstract This paper presents a generic and systematic approach to solve the kinematics of series-parallel (hybrid) robot manipulators. The virtual link concept is a theoretical development to solve the kinematics of hybrid robots using the Denavit-Hartenberg notations. These notations have so far been applicable only to series robots. The virtual link concept employs fictitious serial links, termed “virtual links”, to transform a series-parallel manipulator into an equivalent series manipulator. The kinematics of this transformed series manipulator is solved using Denavit-Hartenberg notations. The results are mapped back to the actual manipulator using kinematic relations between fictitious serial links and the replaced parallel structure of the actual manipulator. This approach appears to be generic and systematic for analyzing the kinematics of series-parallel robot manipulators.