Direct Kinematic Analysis Research Articles

Developing application techniques of kinematics and simulation model for InMoov robot

In this work, the direct and inverse kinematic analysis of both robot arms are investigated based on the analytical and informational representation. The results of the study will be used to provide the functionality of gesturing by a robot in sign language, both Kazakh and other languages, used in educational systems, especially in children's institutions and societies for deaf people. A simulation model of the movement of the robot's arms in the workspace has been studied and built. The developed model will be further implemented and used as mathematical and information support for the created robot. The developed library contains implementations of forward kinematics and iterative algorithms for inverse kinematics. The InMoov robot is a platform widely used in research tasks, supported by the MyRobotLab package. A direct kinematic model for the left and right hands of the robot has been studied. Based on the Python programming language, the working space for robot manipulators was calculated, using the matpilotlib library, an iteration method algorithm was developed to find the probable path of robot manipulators in space. A model of a structured artificial neural network (ANN) is proposed, which is used to find a solution to the inverse kinematics of the InMoov robot with six degrees of freedom (4-dof). The applied ANN model is a multilayer perceptron neural network (MLPNN) in which the learning rule of the Adam-a gradient diskend type is applied. To solve this problem, the problem of finding the best ANN configuration was studied. It has been established that a multilayer parseptron neural network gives the minimum mean square error. The regression coefficient analysis, which shows a 95.6 % fit of all communication variables, is acceptable for obtaining the inverse kinematics of the InMoov robot.

Design and Fabrication of Eight-Legged Spider Using KLANN Mechanism

In the present paper, an attempt has been made to carry out Design and fabrication of eight-legged spider using klann mechanism. A four-revolute (4R) kinematic chain has been chosen for each leg mechanism in order to mimic the leg structure of an insect. Denavit–Hartenberg (D-H) conventions are used to perform kinematic analysis of the eight-legged spider. The direct and inverse kinematic analysis for each leg has been considered in order to develop an overall kinematic model of an eight-legged spider, when it follows a straight path. The problems related to trajectory generation of legs have been solved for both the swing and support phases of the robot. It is important to mention that trajectory generation problem during the support phase has been formulated as an optimization problem and solved using the least squared method. Lagrange-Euler formulation has been utilized to determine the joint torques. The developed kinematic and dynamic models have been examined for tripod gait generation of the eight-legged spider using klann mechanism.

An experimental inverse and direct kinematics analysis of multi-axial simulation table

An experimental inverse and direct kinematics analysis of multi-axial simulation table

An experimental inverse and direct kinematics analysis of multi-axial simulation table

An experimental inverse and direct kinematics analysis of multi-axial simulation table

Direct Kinematic Analysis of the Spatial Parallel Mechanism With 3-R(P)S Structure Based on the Point Pair Relationship

Abstract This paper demonstrates a novel geometric modeling and computational method of the family of spatial parallel mechanisms (PMs) with 3-R(P)S structure for direct kinematic analysis based on the point pair relationship. The point pair relationship, which is derived from the framework of conformal geometric algebra (CGA), consists of the relationship between the point and the point pair and two point pairs. The first research is on the distance relationship between the point and the point pair. Second, the derivation of the distance relationship between two point pairs is based on the aforementioned result, which shows the mathematical homogeneity. Third, two formulations for a point of the point pairs that satisfy the distance relationship between two point pairs are reduced. Fourth, the point pair relationship is applied to solve the direct kinematic analysis of the spatial parallel mechanism with 3-R(P)S structure. Finally, four numerical examples are provided to verify the validity of the proposed algorithm. Overall, the proposed method can be generalized for the direct kinematics of a series of spatial parallel mechanisms with 3-R(P)S structure.

Mínimos Cuadrados Recursivos para un Manipulador que Aprende por Demostración

En este trabajo, se desarrolla un sistema de control automatizado para permitir que un manipulador aprenda y planifique las trayectorias a partir de las demostraciones dadas por la mano de un usuario. La entrada de datos es adquirida por un sensor, y se aprende su comportamiento a través de un algoritmo de aprendizaje automático basado en los mínimos cuadrados recursivos. Se utiliza un perfil de trayectoria de interpoladores a tramos para evitar el movimiento impulsivo del manipulador. Se realiza el análisis de las cinemáticas directa e inversa para obtener los valores de las variables articulares para el manipulador. Se crea un modelo dinámico usando la formulación de Newton-Euler. Se aplica un control proporcional derivativo al sistema. Los sistemas de monitoreo y control se implementan en una plataforma embebida para fines de prueba.

A versatile apparatus for inverse and direct kinematic analysis of 3RR planar parallel mechanisms

The paper presents an approach containing a package of several integrated programs, each of them being devoted to one of the principal problems regarding 3RRR planar parallel mechanisms: workspace, forward and direct kinematics and singularities problem. In order to perform workspaces coordinates and forward kinematics was used classical procedures, widespread and known in technical literature. For direct kinematics and singularities study, we used classical procedures also, but applied in a particular ways, related to each of them. Thereby, the proposed programs package represents a useful instrument in practical goals, one of them being didactical process of students’ instruction in engineering, but also for research and design purposes. The paper is a refined and a extended research of an older one [24].

Back Propagation Method of Artificial Neural Networks for Finding the Position Control of Stanford Manipulator and Direct Kinematic Analysis of Elbow Manipulator

Nowadays the robot technology is advancing rapidly and the use of robots in industries has been increasing. In designing a robot manipulator, kinematicsplays a vital role. The kinematic problem of manipulator control is divided into two types, direct kinematics and inverse kinematics. Robot inverse kinematics, which is important in robot path planning, is a fundamental problem in robotic control. Past solutions for this problem have been through the use of various algebraic or algorithmic procedures, which may be less accurate and time consuming. Artificial neural networks have the ability to approximate highly non-linear functions applied in robot control. The neural network approach deserves examination because of the fundamental properties of computation speed, and they can generalize untrained solutions. In the present work an attempt has been made to evaluate the problemof robot inverse kinematics of Stanford manipulator using artificial neural network approach. Finally two programs are written using C language to solve inverse kinematic problem of Stanford manipulator using Back propagation method of artificial neural network. In this network, the input layer has six nodes, the hidden layer has three nodes, and the output layer has two nodes. And also Elbow manipulator was modelled and its direct kinematics was analysed.

CGA-Based approach to direct kinematics of parallel mechanisms with the 3-RS structure

This paper presents a unified geometric modeling and solution procedure for direct kinematic analysis of a class of parallel mechanisms based on conformal geometric algebra (CGA). After locking the actuated joints, such parallel mechanisms will be turned into a 3-RS structure, which is composed of two triangular platforms connected by three RS serial chains in parallel. Using the proposed approach, the univariate polynomial equation for the direct kinematic analysis of these parallel mechanisms can be derived in three steps. Firstly, the positions of two of the three spherical joints on the moving platform are formulated by the intersection, dissection and dual of the basic geometric entities under the frame of CGA. Secondly, a coordinate-invariant equation expressed in terms of geometric entities is derived via CGA operation. Thirdly, a univariate polynomial equation is obtained directly from the aforementioned coordinate-invariant equation by using tangent-half-angle substitution. Several case studies are then presented to verify the solution procedure. The novelties of this approach lie in that: (1) The formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA; (2) No algebraic elimination procedure is required to derive the univariate polynomial equation; and (3) The proposed approach is applicable to the direct kinematics of this family of parallel mechanisms with any link parameters.

A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

A geometric modeling and solution procedure for direct kinematic analysis of 6-4 Stewart platforms with any link parameters is proposed based on conformal geometric algebra (CGA). Firstly, the positions of the two single spherical joints on the moving platform are formulated by the intersection, dissection, and dual of the basic entities under the frame of CGA. Secondly, a coordinate-invariant equation is derived via CGA operation in the positions of the other two pairwise spherical joints. Thirdly, the other five equations are formulated in terms of geometric constraints. Fourthly, a 32-degree univariate polynomial equation is reduced from a constructed 7 by 7 matrix which is relatively small in size by using a Gröbner-Sylvester hybrid method. Finally, a numerical example is employed to verify the solution procedure. The novelty of the paper lies in that (1) the formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA and (2) the size of the resultant matrix is smaller than those existed.

An approach of topology optimization of multi-rigid-body mechanism

Topology synthesis of multi-rigid-body mechanisms has always been a very important stage in the mechanism design process. In most cases, the topology of the multi-rigid-body mechanism for particular task is obtained by designers’ experience and ingenuity, rather than automatic approach. In this work, an approach of topology optimization of multi-rigid-body mechanisms is investigated. The core process of the approach is an automatic optimization design process. In this approach, we construct kinematics mapping from truss structures to the joint-linked mechanisms, which transforms the topology optimization problem of multi-body system into the truss structure optimization problem. We also develop a new strategy for topology optimization of statically determinate truss, the advantage of which lies in the ability dealing with statically determinate truss topology optimization problem compared to the existing methods. By automatically optimizing the topology of the truss structure, the topology of the multi-rigid-body mechanism is optimized automatically, accordingly. Here, we utilize the investigated approach to design suitable layout for multi-rigid-body micro-displacement amplifying mechanisms (MMAMs) with a large amplification ratio (>50). The layout consists of not only the topology information of the mechanism, but also the dimension parameters of the mechanism. The procedure of the approach is carried out in steps, and a human–computer interaction program has been developed for it. Using the developed program, different MMAMs are achieved. Meanwhile, the direct kinematics analysis of the MMAMs is achieved automatically, the existence of dead point position in the mechanism within movement range is checked and the micro-displacement amplification ratio is calculated out. The computing results are validated by the ADAMS® motion simulation, which proves that the achieved MMAMs fully fulfill the functional requirement. Along with two of the achieved MMAMs, the approach is explained, its functionality is shown, its advantages, limitations, some open problems and future works are discussed.

Associations between tongue movement pattern consistency and formant movement pattern consistency in response to speech behavioral modifications.

The degree of speech movement pattern consistency can provide information about speech motor control. Although tongue motor control is particularly important because of the tongue's primary contribution to the speech acoustic signal, capturing tongue movements during speech remains difficult and costly. This study sought to determine if formant movements could be used to estimate tongue movement pattern consistency indirectly. Two age groups (seven young adults and seven older adults) and six speech conditions (typical, slow, loud, clear, fast, bite block speech) were selected to elicit an age- and task-dependent performance range in tongue movement pattern consistency. Kinematic and acoustic spatiotemporal indexes (STI) were calculated based on sentence-length tongue movement and formant movement signals, respectively. Kinematic and acoustic STI values showed strong associations across talkers and moderate to strong associations for each talker across speech tasks; although, in cases where task-related tongue motor performance changes were relatively small, the acoustic STI values were poorly associated with kinematic STI values. These findings suggest that, depending on the sensitivity needs, formant movement pattern consistency could be used in lieu of direct kinematic analysis to indirectly examine speech motor control.

A KBE tool for solving the mechanisms kinematics

Knowledge-Based-Engineering (KBE) is a research field in which the methodologies and technologies for capturing and re-using the engineering knowledge are studied. Nowadays, the mechanisms design is accomplished by using various CAD software. Since, every CAD system includes KBE tools, those can be used to reduce time and simplify the mechanism's design process.One step in the design of the mechanisms with more than one degree of freedom is the direct and inverse kinematic analysis. This step can be difficult, because many calculations are involved and usually more than one solution exists. The geometrical constraints defined in the CAD system for the mechanism linkage's assembling, offer a simple solution for the kinematics analysis.This paper presents a KBE tool useful for kinematics analysis.The automation of repetitive tasks is implemented in an external application written in C# that it is also presented.

Design and analysis of a reconfigurable parallel mechanism for multidirectional additive manufacturing

Reconfigurable parallel mechanisms (RPMs) have the advantages of high stiffness, good dynamic performance due to their parallel structures, and can reconfigure themselves into various mobility configurations to accommodate different task requirements, which indicate that RPMs have the potential to be used in multidirectional additive manufacturing. Based on this application, this paper focuses on the design and analysis of a novel RPM. Degree of freedom (DOF) requirements in different stages of multidirectional additive manufacturing are analyzed. A hybrid limb that is composed of a planar metamorphic mechanism and a 4-DOF serial chain is presented, and then employed in the design of a three-legged RPM. Unified model for kinematic position analysis and the overall Jacobian matrix of the RPM are established. Singularity analysis including inverse kinematic singularity and direct kinematic singularity analysis are conducted. Workspaces of the RPM in different operation modes are evaluated. A prototype and some experiments are presented.

English

In this paper the mathematic model and kinematics of robotic arm are mainly analyzed. The robotic arm uses the Denavit Hartenberg (D-H) method to determine the parameters with transformation matrices. The direct kinematic analysis was conducted to determine the parameter of robotic arm by using Denavit Hartenberg (D-H) method. The calculated parameters of robotic arm were implemented by direct kinematics and compared with the measured parameter by rotary encoder to determine the accuracy of each parameter.

Structural Synthesis, Work Spaces and Direct Kinematic of the one Serial Kinematic Chain with 8 Axes for Industrial Robots

Abstract In this paper, for a useful working basis, including for the promotion of new redundant structures, beyond those already implemented, there is a systematization of kinematic chain structures with 8 axes. Representation of corresponding workspaces can help the designer in choosing the structure with maximum functionality for a given application. Exemplifying of the use of these redundant structures, namely a structure with 8 axes, is possible presenting the eight-axes robot CLOOS, of type: T⊥R|| (R⊥R||R)(R⊥R⊥R). For this version the workspace is represented, first sequentially, successively for each coupling, starting with the translation coupling from the kinematic chain base and then the workspace is represented totally by overlapping workspaces obtained for each coupling. Below we present the direct kinematics analysis for this kinematic chain using the homogeneous operators’ method. This method is based on the use of homogeneous translation or rotation operators and covering the kinematic chain from the base to the characteristic point at its end by a mobile reference system. Transition from a coupling to another is associated with a matrix homogeneous operator of translation, rotation, translation-translation, rotation-rotation or combined (rotation-translation or translation-rotation). Based on linear and angular dimensions expressed in matrix by corresponding homogeneous operators we obtain the matrix of the robot characteristic point coordinates in the fixed reference system attached to the robot base. Thus, direct kinematics is solved qualitatively. For a set of numerical values, we obtain a quantitative solution.

Biomechanical Aspects of the Lower Limb Positions to the Direct Free Kick at Football

This paper present the aspects regarding the kinematics analysis of the human lower limb, respectively the angular positions and the angular velocities of the body segment, thigh, leg and foot, during of the direct free kick at football. For the analysis were videotaped the direct free kicks of 10 human subjects, children between 10 and 13 years, after which the images were processed using a specialized software. The method of the direct experimental kinematics analysis it allowed the determination of the amplitudes and the angular speeds segmentation advisable for to obtain accurate kicks in the direct free kicks with the ball. Regarding the performance, the objective pursued was that the ball must to have a trajectory on the space of the gate and also exceed the human wall which it is in front of the gate.

The Structure, Work Space and Direct Kinematic of the Robots with 8 Axes of Type T Normal R Parallel (PM)(OM)

The paper presents first structural synthesis aspects of serial redundant open kinematic chains for industrial robots. These chains are obtained from 3-axis positioning kinematic chains that create non-degenerate workspaces plus first a rotation or translation coupling in parallel or perpendicular position, obtaining structures with 7-axis, to which by adding in the same way one more rotation or translation coupling structures with 8 axes are obtained. Below we present the direct kinematics analysis for this kinematic chain using the homogeneous operators’ method. This method is based on the use of homogeneous translation or rotation operators and covering the kinematic chain from the base to the characteristic point at its end by a mobile reference system. Based on linear and angular dimensions expressed in matrix by corresponding homogeneous operators we obtain the matrix of the robot characteristic point coordinates in the fixed reference system attached to the robot base. Thus, direct kinematics is solved qualitatively. For a set of numerical values, ​​we obtain a quantitative solution.

Kinematics, Dynamics and Power Consumption Analyses for Turning Motion of a Six-Legged Robot

This paper deals with kinematics, dynamics and power consumption analyses of a six-legged robot generating turning motions to follow a circular path. Direct and inverse kinematics analysis has been carried out for each leg in order to develop an overall kinematics model of the six-legged robot. It aims to estimate energy-optimal feet forces and joint torques of the six-legged robot, which are necessary to have for its real-time control. To determine the optimum feet forces, two approaches are developed, such as minimization of norm of feet forces and minimization of norm of joint torques using a least square method, and their performances are compared. The developed kinematics and dynamics models are tested through computer simulations for generating turning motion of a statically stable six-legged robot over flat terrain with four different duty factors. The maximum values of feet forces and joint torques decrease with the increase of duty factor. A power consumption model has been derived for the statically stable wave gaits to minimize the power requirement for both optimal foot force distributions and optimal foot-hold selection. The variations of average power consumption with the height of the trunk body and radial offset have been analyzed in order to find out energy-optimal foothold. A parametric study on energy consumption has been carried out by varying angular velocity of the robot to minimize the total energy consumption during locomotion. It has been found that the energy consumption decreases with the increase of angular velocity for a particular traveled distance.

Dynamics and Optimal Feet Force Distributions of a Realistic Four-legged Robot

This paper presents a detailed dynamic modeling of realistic four-legged robot. The direct and inverse kinematic analysis for each leg has been considered in order to develop an overall kinematic model of the robot, when it follows a straight path. This study also aims to estimate optimal feet force distributions of the said robot, which is necessary for its real-time control. Three different approaches namely, minimization of norm of feet forces (approach 1), minimization of norm of joint torques (approach 2) and minimization of norm of joint power (approach 3) have been developed. Simulation result shows that approach 3 is more energy efficient foot force formulation than other two approaches. Lagrange-Euler formulation has been utilized to determine the joint torques. The developed dynamic models have been examined through computer simulation of continuous gait of the four-legged robot.