Serial Kinematic Chains Research Articles

Kinematics and optimization of a novel 4-DOF two-limb gripper mechanism

AbstractThis study presents a novel 4-DOF two-limb gripper mechanism with a simple design that offers high adaptability for different objects. The mechanism integrates a three-finger end effector and employs a 2-DOF driving system in both serial kinematic chains mounted on the base, addressing performance problems caused by moving actuators. First, the architecture of the gripper mechanism is described, and its mobility is verified. Next, the inverse and forward kinematic problems are solved, and the Jacobian matrix is derived to analyze the singularity conditions. The inverse and forward singularity surfaces are plotted. The workspace is investigated using a search method, and two indices, manipulability and dexterity, are studied. The proposed manipulator’s parameters are optimized for improved dexterity. The novel gripper mechanism has high potential for grasping different types of parts within a large workspace, making it a valuable addition to the field of robotics.

Type synthesis of serial kinematic chains with screw type terminal constraints based on an adding joint method

Serial kinematic chains(SKCs) with screw type terminal constraints are ubiquitous. However, the type synthesis of such mechanisms has not been systematically studied. Unlike the SKCs which only have pure constraint forces and torques, these kinds of SKCs contain independent screw type terminal constraints with non-zero pitch. This paper develops a systematic work for the type synthesis of general SKCs with terminal screw type constraints. In this paper, combined with the screw theory and the atlas method, the principle and steps for synthesizing SKCs based on an adding joint method are proposed. To derive feasible SKCs with terminal screw type constraints, the concept of constraint-kinematic identification graph(CKIG) is proposed and used to identify the screw type constraints in SKCs. Based on the proposed approach, varied 4R, 3R1P and 2R2P SKCs with 1F1H and 1C1H type terminal constraints and numerous 5R, 4R1P and 3R2P SKCs with 1H type terminal constraint are obtained. In addition, some examples for constructing novel parallel mechanisms(PMs) using the derived SKC with screw type terminal constraints are given. This paper provides an effective method for the type synthesis of SKCs with screw type terminal constraints.

Planar and spherical four-bar linkage [formula omitted] algebraic input–output equations

The algebraic polynomial input–output (IO) equations relating any two of the relative joint displacement parameters, called vi and vj, between any of the six distinct pairs of rigid links in arbitrary planar and spherical four-bar mechanisms are derived. First, the forward kinematics transformation matrices of the corresponding serial kinematic chains are computed in terms of their Denavit–Hartenberg parameters, but with all angles converted to tangent half-angle parameters. These matrices are mapped to their corresponding Study soma coordinates. The serial kinematic chain is closed by equating the soma coordinates to the identity array. Algebraic polynomial elimination methods are then used to obtain a single polynomial in terms of only the design and the selected IO joint displacement parameters. This yields six independent algebraic IO Equations for each of the planar and spherical 4R linkages; the same techniques are applied to derive six additional algebraic IO equations for each of the RRRP and PRRP planar linkages providing a catalogue of 24. The utility of these IO equation sets is demonstrated via discussion of the associated mobility and design parameter spaces.

Simultaneous Calibration of Multiple Revolute Joints for Articulated Vision Systems via SE(3) Kinematic Bundle Adjustment

We propose a vision-based approach to calibrate kinematic structure of low degree-of-freedom (DoF) articulated systems. Standard hand-eye calibration yields excellent eye-to-hand relations by explicitly estimating end-effector mounted camera poses from the Perspective-n-Point (PnP) problem of a single calibration rig. However, these methods struggle when the ideal kinematic model is unknown or inaccurate, which are typical in customized serial chains such as articulated vision systems. Inspired by bundle adjustment in structure-from-motion methods, we proposed an approach, dubbed KBA, to simultaneously localize multiple joint axes at the kinematic level instead of in the 3D space. To achieve this, we design a robust multi-checkerboard detector to enlarge the kinematic coverage of end-effector samples, which are usually limited by sensor field of view. The overall optimization problem is formulated and solved using Lie group SE(3)—suitable for integration into simultaneous localization and mapping systems. In addition to simulated scenes, the experimental results with articulated monocular (AMV) and binocular vision (ABV) confirm that the proposed method not only is applicable to real serial kinematic chains but also enables challenging 3D vision tasks such as stereo reconstruction in motion.

A Recursive Algorithm for the Forward Kinematic Analysis of Robotic Systems Using Euler Angles

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

Dynamics of parallel manipulators with hybrid complex limbs — Modular modeling and parallel computing

Parallel manipulators, also called parallel kinematics machines (PKM), enable robotic solutions for highly dynamic handling and machining applications. The safe and accurate design and control necessitates high-fidelity dynamics models. Such modeling approaches have already been presented for PKM with simple limbs (i.e. each limb is a serial kinematic chain). A systematic modeling approach for PKM with complex limbs (i.e. limbs that possess kinematic loops) was not yet proposed despite the fact that many successful PKM comprise complex limbs.This paper presents a systematic modular approach to the kinematics and dynamics modeling of PKM with complex limbs that are built as serial arrangement of closed loops. The latter are referred to as hybrid limbs, and can be found in almost all PKM with complex limbs, such as the Delta robot. The proposed method generalizes the formulation for PKM with simple limbs by means of local resolution of loop constraints, which is known as constraint embedding in multibody dynamics. The constituent elements of the method are the kinematic and dynamic equations of motions (EOM), and the inverse kinematics solution of the limbs, i.e. the relation of platform motion and the motion of the limbs. While the approach is conceptually independent of the used kinematics and dynamics formulation, a Lie group formulation is employed for deriving the EOM. The frame invariance of the Lie group formulation is used for devising a modular modeling method where the EOM of a representative limb are used to derived the EOM of the limbs of a particular PKM. The PKM topology is exploited in a parallel computation scheme that shall allow for computationally efficient distributed evaluation of the overall EOM of the PKM. Finally, the method is applied to the IRSBot-2 and a 3RR[2RR]R Delta robot, which is presented in detail.

Design and analysis of novel kinematically redundant reconfigurable generalized parallel manipulators

A conventional parallel manipulator (PM) generally employs independent serial kinematic chains to support one rigid moving platform. Compared with PMs, generalized parallel manipulators (GPMs) with configurable platforms can improve the kinematic performance and functionality. This paper highlights the idea of designing and analyzing novel GPMs with configurable platforms. Firstly, the type synthesis of GPMs is performed. Then a novel class of reconfigurable GPMs with remotely operated grippers is constructed. Secondly, the motion-screw system and the reconfiguration property of the manipulator are analyzed based on screw theory. Moreover, the position analysis of the GPM is carried out to evaluate the workspace and reveal the motion characteristics. Furthermore, the numerical examples and simulation results are obtained to demonstrate the presented methodology. The feasible arrangement of the actuated joints is studied and the potential application of the GPM is discussed. Finally, a prototype is manufactured to illustrate the advocated design philosophy and the functionality of the GPM.

Inverse and forward kinematics and workspace analysis of a novel 5-DOF (3T2R) parallel–serial (hybrid) manipulator

The proposed study provides a solution of the inverse and forward kinematic problems and workspace analysis for a five-degree-of-freedom parallel–serial manipulator, in which the parallel kinematic chain is made in the form of a tripod and the serial kinematic chain is made in the form of two carriages displaced in perpendicular directions. The proposed manipulator allows to realize five independent movements—three translations and two rotations motion pattern (3T2R). Analytical relationships between the coordinates of the end-effector and five controlled movements provided by manipulator’s drives (generalized coordinates) were determined. The approach of reachable workspace calculation was defined with respect to available design constraints of the manipulator based on the obtained algorithms of the inverse and forward kinematics. Case studies are considered based on the obtained algorithms of inverse and forward kinematics. For the inverse kinematic problem, the solution is obtained in accordance with the given laws of position and orientation change of the end-effector, corresponding to the motion along a spiral-helical trajectory. For the forward kinematic problem, various assemblies of the manipulator are obtained at the same given values of the generalized coordinates. An example of reachable workspace designing finalizes the proposed study. Dimensions and extreme values of the end-effector orientation angles are calculated.

Inverse Kinematics Data Adaptation to Non-Standard Modular Robotic Arm Consisting of Unique Rotational Modules

The paper describes the original robotic arm designed by our team kinematic design consisting of universal rotational modules (URM). The philosophy of modularity plays quite an important role when it comes to this mechanism since the individual modules will be the building blocks of the entire robotic arm. This is a serial kinematic chain with six degrees of freedom of unlimited rotation. It was modeled in three different environments to obtain the necessary visualizations, data, measurements, structural changes measurements and structural changes. In the environment of the CoppeliaSim Edu, it was constructed mainly to obtain the joints coordinates matching the description of a certain spatial trajectory with an option to test the software potential in future inverse task calculations. In Matlab, the model was constructed to check the mathematical equations in the area of kinematics, the model’s simulations of movements, and to test the numerical calculations of the inverse kinematics. Since the equipment at hand is subject to constant development, its model can also be found in SolidWorks. Thus, the model’s existence in those three environments has enabled us to compare the data and check the models’ structural designs. In Matlab and SolidWorks, we worked with the data imported on joints coordinates, necessitating overcoming certain problems related to calculations of the inverse kinematics. The objective was to compare the results, especially in terms of the position kinematics in Matlab and SolidWorks, provided the initial joint coordinate vector was the same.

A numeric derivation for fast regressive modeling of manipulator dynamics

We present Pseudo-Symbolic Dynamic Modeling (PSDM), a novel method of deriving the closed-form equations of motion of a serial kinematic chain, using base inertial parameters. PSDM is a numerical algorithm, yet allows for model simplification and pre-computation generally only possible using symbolic software. In PSDM, we characterize the form of the dynamic equations to build a set of functions guaranteed to form a linear basis for the inverse dynamics function of the manipulator. Then, a two-step numerical analysis is performed to reduce this set into a minimal dynamic model, in regressor form. PSDM offers a fast and procedural method of generating simplified dynamic models. Extensions to the algorithm allow for fast real-time code generation, forward dynamic modeling, and increased model efficiency through the elimination of minimally important model elements. The algorithm is benchmarked on common robot configurations and shown to be attractive for the dynamic modeling of up to 7-DOF manipulators, in terms of derivation time and real-time evaluation speed. Additionally, a MATLAB implementation of the algorithm has been developed and is made available for general use.

Design and Error Evaluation of Planar 2DOF Remote Center of Motion Mechanisms With Cable Transmissions

Abstract In a minimally invasive surgical (MIS) robot, the remote center of motion (RCM) mechanism is usually used to realize the constrained motion of the surgical instrument. In this paper, a novel design method for planar 2DOF RCM mechanisms is proposed based on closed-loop cable transmissions. The concept is to utilize several coupled cable transmissions to constrain a serial kinematic chain. Through the analysis and determination of the transmission ratios for these cable transmissions, a class of planar 2DOF RCM mechanisms without any active or passive translational joints is obtained, which provides large workspace and low collision risk for the MIS robots. One of the resulting mechanisms is designed in detail and kinematically analyzed. To evaluate the influence of the elastic cables, a new error model for the proposed RCM mechanism is established through the static analysis and cable deformation analysis. Utilizing this model, the cable-induced error distributions of the tip and the RCM point are obtained, which show that these errors are within a relatively small range. Furthermore, the prototype of the proposed mechanism is built, and the accuracy experiments are conducted.

A novel class of generalized parallel manipulators with high rotational capability

A conventional parallel manipulator is characterized by connecting one moving platform with two or more serial kinematic limbs. Since each limb is independently supporting one moving platform, the moving platform must be a rigid body with several kinematic pairs fixed on it. However, for generalized parallel manipulators with articulated moving platforms, the moving platforms are not limited to rigid bodies but including serial kinematic chains or internal kinematic joints. The introduction of articulated moving platforms allows for improving the kinematic performance of generalized parallel manipulators, especially for rotational capability. On account of the structural characteristics of the moving platforms, it also poses a significant challenge in the construction of the structures of manipulators. This research raises a new method for the type synthesis of generalized parallel manipulators with novel articulated moving platforms. The proposed method introduces a striking shortcut for the limb structure analysis of mechanisms with high rotational capability. In this paper, a class of generalized parallel manipulator with different degrees of freedom from 3 to 6 are constructed by using the constraint synthesis method, and several examples are provided to demonstrate the feasibility of the advocated method. At last, the 3T3R generalized parallel manipulator is taken as an example to analyze the inverse kinematics, and the evaluation of the workspace is conducted to verify the rotational capacity.

Jacobian approach to the kinestatic analysis of a full vehicle model with application to cornering motion analysis

The Jacobian approach to the kinestatic analysis of a planar suspension mechanism has been previously presented. In this paper, the theory is extended to three-dimensional kinestatic analysis by developing a full kinematic model and viewing it as a spatial parallel mechanism. The full kinematic model consists of two pairs of the front (double wishbone) and rear (multi-link) suspension mechanisms together with a newly developed ground-wheel contact model. The motion of each wheel of four suspension mechanisms is represented by the corresponding instantaneous screw at any instant. A vehicle is considered to be a 6-degrees-of-freedom spatial parallel mechanism whose vehicle body is supported by four serial kinematic chains. Each kinematic chain consists of a virtual instantaneous screw joint and a kinematic pair representing ground-wheel contact model. The kinestatic equation of the 6-degrees-of-freedom spatial parallel mechanism is derived in terms of the Jacobian. As an important application, a cornering motion of a vehicle is analysed under the assumption of steady-state cornering. A numerical example is presented to illustrate how to determine the optimal locations of strut springs for the least roll angle in cornering motion using the proposed method.

An Adaptive Second Order Sliding Mode Inverse Kinematics Approach for Serial Kinematic Chain Robot Manipulators

The problem of inverse kinematics is essential to consider while dealing with the robot’s mechanical structure in almost all applications. Since the solution of the inverse kinematics problem is very complex, many research efforts have been working towards getting the approximate solution of this problem. However, for some applications, working with the approximate robot’s model is neither sufficient nor efficient. In this paper, an adaptive inverse kinematics methodology is developed to solve the inverse kinematics problem in such a way that compensate for unknown uncertainty in the Jacobian matrix of the serial kinematic chain robot manipulators. The proposed methodology is based on continuous second order sliding mode strategy (CSOSM-AIK). The salient advantage of the CSOSM-AIK approach is that it does not require the availability of the kinematics model or Jacobian matrix of the robot manipulators from joint space variables to Cartesian space variables. The global stability of the closed-loop system with CSOSM-AIK methodology is proven using the Lyapunov theorem. In order to demonstrate the robustness and effectiveness of the proposed methodology, some simulations are conducted.

Párhuzamos kinematikájú billenőasztal elemzése

Examining modern five-axis milling machines, it can be concluded that the structural variants lead to machines with different constructions. The variants are mainly determined by the dimensions of the workpieces that can be manufactured on the machine and the kinematic structure of the machine. Based on the kinematic chain of the machine, a distinction can be made between serial kinematic, parallel kinematic and hybrid kinematic chain variants. On simultaneous five-axis machining, the tool and the workpiece perform linear and orientational movements relative to each other simultaneously. In this paper an analysis of variant of a tilting table with parallel kinematics is presented.

Dynamics Modeling of Topologically Simple Parallel Kinematic Manipulators: A Geometric Approach

Abstract Dynamics modeling is indispensable for the design and control of dexterous parallel kinematic manipulators/machines (PKM). Various modeling approaches proposed in the literature build upon the classical formulations for serial manipulators, and thus, inherit those modeling conventions that tend to be restrictive rather than user-friendly. Moreover, the special kinematic topology of PKM is treated either ad hoc or by resolving loop constraints using standard methods from multibody dynamics. Geometric formulations on the other hand, more precisely Lie group formulations, were developed over the last decades that provide a flexible and user-friendly approach to the modeling of robotic systems in general. A dedicated formulation for topologically simple PKM has not yet been proposed, however. Such a formulation is presented in this paper. The frame invariance of the geometric formulation gives rise to a modular modeling approach that further reduces the modeling effort. The equations of motion (EOM) in terms of task space coordinates as well as in actuator coordinates are presented for kinematically nonredundant and redundant topologically simple PKMs. A PKM is topologically simple if its moving platform is connected to the base by simple serial kinematic chains and if there are no other kinematic chains than these. The majority of PKMs are topologically simple, including fully parallel PKM. Applications of the EOM for dynamics simulation and model-based control are briefly discussed. The paper also provides a literature review of approaches to dynamics modeling of PKM.

A screw theory based approach to determining the identifiable parameters for calibration of parallel manipulators

Establishing complete, continuous and minimal error models is fundamentally significant for the calibration of robotic manipulators. Motivated by practical needs for models suited to coarse plus fine calibration strategies, this paper presents a screw theory based approach to determining the identifiable geometric errors of parallel manipulators at the model level. The paper first addresses two specific issues: (1) developing a simple approach that enables all encoder offsets to be retained in the minimal error model of serial kinematic chains; and (2) exploiting a fully justifiable criterion that allows the detection of the unidentifiable structural errors of parallel manipulators. Merging these two threads leads to a new, more rigorous formula for calculating precisely the number of identifiable geometric errors, including both encoder offsets and identifiable structural errors, of parallel manipulators. It shows that the identifiability of structural errors in parallel manipulators depends highly upon joint geometry and actuator arrangement of the limb involved. The process is used to determine the unidentifiable structural errors of two lower mobility parallel mechanisms to illustrate the effectiveness of the proposed approach.

Different Kinds of 3T2R Serial Kinematic Chains and Their Applications in Synthesis of Parallel Mechanisms

This paper proposes a new-kind three-translational and two-rotational (3T2R) motion with one fixed and one variable rotation directions. The serial kinematic chains (SKCs) that generate the proposed motions are synthesized. They are quite different from the SKCs generating 3T2R motion with two fixed rotation directions. Firstly, according to the relationships between the two rotations in a motion, the classification of 3T2R motions is discussed. By using finite screw as mathematical tool, the expressions of the two different kinds of 3T2R motions are formulated as algebraic sets. Secondly, serial motion generators of the 3T2R motions are investigated. The SKCs that generate the first-kind 3T2R motion are briefly reviewed; the twenty-eight types of SKCs that generate the second-kind 3T2R motion are synthesized by analytical derivations. Finally, the SKCs with the second-kind 3T2R motion are used to synthesize new parallel mechanisms. Two five-degree-of-freedom (five-DoF) systematical parallel mechanisms are taken as examples to show the applications of these SKCs. This paper provides theoretical foundations for the research on motions generated by complex SKCs and on motion patterns with variable rotation directions and centers.

Reconfiguration Analysis of a 3-DOF Parallel Mechanism

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

Sensory Fusion of Magnetoinertial Data Based on Kinematic Model With Jacobian Weighted-Left-Pseudoinverse and Kalman-Adaptive Gains

This paper presents a sensory fusion method for estimation of joint angles of serial kinematic chains with rotational degrees of freedom based on magnetoinertial measurements—Magnetoinertial tracking based on JAcobian PseudoInverse (MIJAPI). The concept takes into account the mechanism kinematic model, and the computation relies on the differential kinematics inversion (inverse kinematics solution based on the Jacobian inverse). A Moore–Penrose weighted left pseudoinverse of the mechanism Jacobian matrix is applied to solve a (typically) overdetermined system (redundant measurements resulting from constraints related to attachments of magnetoinertial sensors) in a least-squares approach. Calculation of a gain matrix for correcting the estimated angles is based on Kalman-adaptive algorithm. The quality of the proposed approach was compared to different solutions based on the Unscented Kalman filter. In terms of computational complexity, the MIJAPI concept outperforms the Kalman-based approaches. Better results were also noticed in conditions with significant measurement disturbances and sensor misalignments. The method is applicable in the fields of human motion tracking/analysis as well as robotics.