Four Novel Pick-and-Place Isoconstrained Manipulators and Their Inverse Kinematics

2010 ◽  
Author(s):  
Po-Chih Lee ◽  
Jyh-Jone Lee ◽  
Chung-Ching Lee
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Industrial Assembly ◽  
Pick And Place ◽  
The Matrix ◽  
Potential Applications ◽  
Algebra Method ◽  
Pick And Place Operation

The four-degree-of-freedom (4-DoF) Schoenflies-motion (briefly termed X-motion) manipulator with the fast pick-and-place operation is essential for industrial assembly and packaging. For the development of this kind of industrial manipulator, we provide architectures and inverse kinematics of four X-motion isoconstrained parallel mechanisms with two limbs, CuuUwHw-//-CvvUwHw, CuRuuUhw-//-CvRvvUhw, CuRuPHw-//-CvRvPHw and CuPuUhw-//-CvPvUhw (R, P, H and C denote revolute, prismatic, screw and cylindrical pairs respectively; U indicates a universal joint). These novel manipulators are excerpted from numerous general architectural types of isoconstrained parallel generators of X-motion. In this work, their architectures and mobility are first elucidated in detail. With the help of the well-known D-H symbolic notations, their three translational and one rotational motion are comprehensively verified through the four-by-four coordinate transformation matrix approach. Inverse kinematic solutions of joint displacements of each manipulator are further established by using the matrix algebra method for the reference of potential applications.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Author(s):  
Zhi Xin Shi ◽  
Yu Feng Luo ◽  
Lu Bing Hang ◽  
Ting Li Yang
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Algebraic Method ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Parallel Mechanisms ◽  
Simple Method ◽  
Inverse Kinematics Problem ◽  
Serial Robot

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

scholarly journals Type synthesis and kinematics analysis of a family of three translational and one rotational pick-and-place parallel mechanisms with high rotational capability

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985307
Author(s):  
Xing Zhang ◽  
Dejun Mu ◽  
Yuze Liu ◽  
Jie Bi ◽  
Hongrui Wang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Type Synthesis ◽  
Lie Group Theory ◽  
Revolute Joints ◽  
Pick And Place ◽  
Pick And Place Operation

This article proposes a family of spatial three translational and one rotational parallel mechanisms (PMs) for pick-and-place operation. Their features are one independent rotation of the mechanism with four identical limbs, which are provided by the four revolute joints on the moving platform. The rotational capability of the PMs has a range of at least 180°. This article focuses on the synthesis of the PMs and kinematics analysis of the 4- P(2-SS)R parallel mechanism. First, based on the Lie group theory, three parallelograms are used in designing the PMs. The limbs are listed and two types of three translational and one rotational PMs are synthesized. Then, a typical 4- P(2-SS)R PM is selected, the 6 × 6 Jacobian matrix and the 6 × 6 × 6 Hessian matrix of the mechanism are derived for solving the displacement, velocity, and acceleration of the mechanism. Finally, singularity configurations are disclosed from the 6 × 6 Jacobian matrix, and the workspace of the mechanism is provided to illustrate the high rotational capability.

scholarly journals Inverse kinematic analysis of 4 DOF pick and place arm robot manipulator using fuzzy logic controller

2020 ◽  
Vol 10 (2) ◽  
pp. 1376
Author(s):  
Tresna Dewi ◽  
Siti Nurmaini ◽  
Pola Risma ◽  
Yurni Oktarina ◽  
Muhammad Roriz
Keyword(s):  
Fuzzy Logic ◽  
Inverse Kinematics ◽  
Fuzzy Logic Controller ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Experimental Results ◽  
Position Errors ◽  
Motion System ◽  
Pick And Place ◽  
The Right

The arm robot manipulator is suitable for substituting humans working in tomato plantation to ensure tomatoes are handled efficiently. The best design for this robot is four links with robust flexibility in x, y, and z-coordinates axis. Inverse kinematics and fuzzy logic controller (FLC) application are for precise and smooth motion. Inverse kinematics designs the most efficient position and motion of the arm robot by adjusting mechanical parameters. The FLC utilizes data input from the sensors to set the right position and motion of the end-effector. The predicted parameters are compared with experimental results to show the effectiveness of the proposed design and method. The position errors (in x, y, and z-axis) are 0.1%, 0.1%, and 0.04%. The rotation errors of each robot links (θ1, θ2, and θ3) are 0%, 0.7% and 0.3%. The FLC provides the suitable angle of the servo motor (θ4) responsible in gripper motion, and the experimental results correspond to FLC’s rules-based as the input to the gripper motion system. This setup is essential to avoid excessive force or miss-placed position that can damage tomatoes. The arm robot manipulator discussed in this study is a pick and place robot to move the harvested tomatoes to a packing system.

Inverse Kinematics of General 4R2P, 3R3P, 4R1C, 2R2C, and 3C Serial Manipulators

1992 ◽  
Author(s):  
Dilip Kohli ◽  
Michael Osvatic
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Serial Manipulators ◽  
Linearly Independent ◽  
The Matrix ◽  
Half Angle ◽  
Inverse Kinematics Problem ◽  
Joint Variable ◽  
General Geometry ◽  
Solution Methodology

Abstract This paper presents a solution to the inverse kinematics problem for 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators of general geometry. The method used to solve these is based on a technique recently presented by the authors for solving the inverse kinematics of general 6R and 5R1P manipulators. In the 6R and 5R1P cases, the method initially starts using 14 linearly independent equations where as for the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulator only 3, 6, 7 or 10 linearly independent equations are required, depending on the case. Through the use of a linearization and dialytic elimination method all 4R2P, 3R3P, 4R1C, 2R2C and 3C cases are reduced to equating to zero the determinant of a matrix whose elements are linear in the tangent of a half angle of a joint variable. The size of this matrix is (8 × 8) for all 4R2P manipulators, (2 × 2) for all 3R3P and 3C manipulators, (16 × 16) for 4R1C manipulators, (4 × 4) for RCRC and CRCR manipulators and (8 × 8) for the remaining 2R2C manipulators providing 8th, 2nd, 16th, 4th and 8th degree inverse kinematic polynomial respectively. Thus, the determinant equated to zero gives us the characteristic equation of the degree expected. The unique form of the matrix allows us to obtain the solution by solving an eigenvalue problem. Many variations of the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators are presented and the solution methodology is illustrated by several numerical examples.

One Novel Isoconstrained Parallel Robot With Schoenflies-Motion

2013 ◽  
Author(s):  
Po-Chih Lee
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Point Of View ◽  
Universal Joint ◽  
Small Motion ◽  
Robot Architecture ◽  
Pick And Place ◽  
Pick And Place Operation

The coupling between two opposite bars of the hinged parallelogram produces relative 1-DoF circular translation and the opposite bars can move but remain parallel. From the point of view of kinematics, a hinged parallelogram is equivalent to a prismatic pair for a small motion. On the basis of a special parallel mechanism with the limb architecture of type CPUh (C and P denote cylindrical and prismatic pairs; Uh indicates the pseudo-universal-joint having one revolute and one screw pairs with the intersecting axes), we provide one novel Schoenflies-motion isoconstrained CPaUh//CPaUh robot with only two limbs having the hinged parallelograms for the fast pick-and-place operation of the assembly and packaging applications. This type of robot is compact for not only its structure but also its actuation. The robot architecture and kinematics including inverse and forward solutions are studied. In addition, Jacobian matrix, singularity analysis and workspace are further discussed. It is hoped that the evaluations of such two-limb parallel mechanism can be useful for possible application in industry where pick-and-place motion and higher accuracy are required.

Design and Analysis of 3R2T and 3R3T Parallel Mechanisms With High Rotational Capability

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Congzhe Wang ◽  
Yuefa Fang ◽  
Sheng Guo
Keyword(s):  
Inverse Kinematics ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Velocity Analysis ◽  
Parallel Mechanisms ◽  
Workspace Analysis ◽  
Moving Platform ◽  
Displacement Theory ◽  
Lie Subgroup ◽  
Orientation Workspace

This paper describes the design, kinematics, and workspace analysis of 3R2T and 3R3T parallel mechanisms (PMs) with large rotational angles about three axes. Since the design of PMs with high rotational capability is still a challenge, we propose the use of a new nonrigid (or articulated) moving platform with passive joints in order to reduce the interference between limbs and the moving platform. According to the proposed nonrigid platform and Lie subgroup of displacement theory, several 3R2T and 3R3T PMs are presented. Subsequently, the inverse kinematics and velocity analysis of one of the proposed mechanisms are detailed. Based on the derived inverse kinematic model, the constant-orientation workspace is computed numerically. Then, the analysis of rotational capability about the three axes is performed. The result shows that even if interference and singularity are taken into account, the proposed mechanisms still reveal the high continuously rotational capability about the three axes, by means of actuation redundancy.

Kinematics of a 3-DOF Translational Parallel Mechanism With 3-PRPaR Topology

2004 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jeng-Hong Chou
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Translational Motion ◽  
Analytical Form ◽  
Inverse Kinematic ◽  
Closed Form Solutions ◽  
The Matrix ◽  
Six Dof ◽  
Singular Configuration ◽  
Algebra Method

From the standpoint of kinematics, we present a type of three-dof pure spatial translational parallel mechanism with 3-PRPaR topology as an alternative to design automation devices and a regional structure of a six-dof hybrid parallel platform. First, we describe the structural properties of mechanism and analyze its kinematic mobility. It is verified that a pure translational motion does exist through the coordinate transformation technique and the well-known D-H parametric notations. Then, we proceed with the forward and inverse kinematic analysis and derive their analytical closed-form solutions by the matrix algebra method. For the confirmation of the derived equations, some numerical examples are also taken. Furthermore, with the help of the forward kinematics, we derive the workspace in the analytical form. Finally, taking account of the overall Jacobian matrix provides the condition number and the identification of singular configuration is explored based on direct and inverse kinematics Jacobian matrix.

scholarly journals Development of a Decellularized Porcine Esophageal Matrix for Potential Applications in Cancer Modeling

Cells ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 1055
Author(s):  
Hersh Chaitin ◽  
Michael L. Lu ◽  
Michael B. Wallace ◽  
Yunqing Kang
Keyword(s):  
Cell Growth ◽  
Lymphatic Vessels ◽  
Significant Loss ◽  
Cancer Cell Growth ◽  
Cell Growth And Migration ◽  
Decellularized Extracellular Matrix ◽  
Cancer Models ◽  
The Matrix ◽  
Potential Applications ◽  
And Migration

Many decellularized extracellular matrix-derived whole organs have been widely used in studies of tissue engineering and cancer models. However, decellularizing porcine esophagus to obtain decellularized esophageal matrix (DEM) for potential biomedical applications has not been widely investigated. In this study a modified decellularization protocol was employed to prepare a porcine esophageal DEM for the study of cancer cell growth. The cellular removal and retention of matrix components in the porcine DEM were fully characterized. The microstructure of the DEM was observed using scanning electronic microscopy. Human esophageal squamous cell carcinoma (ESCC) and human primary esophageal fibroblast cells (FBCs) were seeded in the DEM to observe their growth. Results show that the decellularization process did not cause significant loss of mechanical properties and that blood ducts and lymphatic vessels in the submucosa layer were also preserved. ESCC and FBCs grew on the DEM well and the matrix did not show any toxicity to cells. When FBS and ESCC were cocultured on the matrix, they secreted more periostin, a protein that supports cell adhesion on matrix. This study shows that the modified decellularization protocol can effectively remove the cell materials and maintain the microstructure of the porcine esophageal matrix, which has the potential application of studying cell growth and migration for esophageal cancer models.

Automatic Planning of Smooth Trajectories for Pick-and-Place Operations

1991 ◽  
Author(s):  
Clément M. Gosselin ◽  
Ammar Hadj-Messaoud
Keyword(s):  
Joint Space ◽  
Inverse Kinematic ◽  
Planning Problem ◽  
Inverse Kinematic Problem ◽  
Polynomial Solutions ◽  
Joint Coordinates ◽  
Pick And Place ◽  
Lift Off ◽  
The Relationship ◽  
Third Derivative

Abstract This paper proposes some new polynomial solutions to the trajectory planning problem encountered in pick-and-place operations. When a robotic manipulator is used for such operations, it is possible to plan the required trajectory in joint space, provided that the inverse kinematic problem has been solved for the initial and final configurations — and possibly for a lift-off and a set-down configuration — and that the workspace is free of obstacles. Polynomial solutions to this problem can be found in the literature. However, they usually provide continuity up to the second derivative only, leading to a discontinuous jerk. The solutions derived in this paper preserve the continuity of the third derivative of the joint coordinates, thereby ensuring smooth trajectories with smooth variations of the actuator currents. Moreover, whenever possible, unique polynomial expressions valid between the initial and final configurations are used in order to simplify the logic. Polynomial formulations without lift-off and set-down configurations are first presented. Then, these intermediate configurations are introduced, leading to a new set of solutions. A global algorithm is then discussed in order to clearly indicate the relationship between the different solutions. Finally, an example illustrating the application to a pick-and-place operation is solved.

A Sensitivity Analysis Based Method for Robot Calibration

1992 ◽  
Author(s):  
S. Kaizerman ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
G. Zak
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

Abstract A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two degree of freedom revolute-joint planar manipulator.

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