A Class of Parallel Manipulators Based on Kinematically Simple Branches

1994 ◽  
Vol 116 (3) ◽  
pp. 908-914 ◽  
Author(s):  
R. P. Podhorodeski ◽  
K. H. Pittens
Keyword(s):  
Parallel Manipulators ◽  
Parallel Structure ◽  
End Effector ◽  
Forward Displacement ◽  
Parallel Class ◽  
Serial Chain ◽  
Order Polynomial ◽  
Six Dof ◽  
Actuated Joints ◽  
Chain Branch

Parallel manipulators consisting of serial branches acting in parallel on a common end effector are examined. All nonredundant, six DOF manipulators corresponding to this in-parallel class of structures are enumerated. A specific in-parallel structure, three branches with two actuated joints per branch (3–2,2,2), is chosen as most promising based upon performance considerations. A class of kimematically simple (KS) serial-chain branch joint layouts suitable for the chosen in-parallel structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled in-parallel manipulator chain are used to show that there exist only five unique branch joint-layouts belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for in-parallel manipulators based on the KS branches can be expressed in a closed form. Furthermore, the 3–2,2,2 in-parallel manipulators are shown to belong to a family of manipulators whose forward displacement solutions can be resolved through roots of a 16th order polynomial.

A Class of Hybrid-Chain Manipulators Based on Kinematically Simple Branches

1992 ◽  
Author(s):  
Ron P. Podhorodeski ◽  
Kenneth H. Pittens
Keyword(s):  
Hybrid Structure ◽  
Chain Structure ◽  
Hybrid Structures ◽  
End Effector ◽  
Forward Displacement ◽  
Serial Chain ◽  
Hybrid Manipulator ◽  
Order Polynomial ◽  
Six Dof ◽  
Specific Hybrid

Abstract Hybrid-chain manipulators consisting of serial branches acting in parallel on a common end effector are examined. All non-redundant, six DOF hybrid manipulator structures are enumerated and a specific hybrid-chain structure is chosen as most promising based upon performance considerations. A class of kinematically simple (KS) serial-chain branches suitable for the chosen hybrid structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled hybrid chain are used to show that there exist only five unique branch structures belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for hybrid structures based on the KS branches can be expressed in a closed form. Furthermore, the KS based hybrid-chains are shown to belong to a family of manipulator structures whose forward displacement solutions can be resolved through roots of a 16th order polynomial.

FORCE-UNCONSTRAINED POSES FOR PARALLEL MANIPULATORS WITH REDUNDANT ACTUATED BRANCHES

2005 ◽  
Vol 29 (3) ◽  
pp. 343-356 ◽  
Author(s):  
Flavio Firmani ◽  
Ron P. Podhorodeski
Keyword(s):  
Dimensional Space ◽  
Parallel Manipulators ◽  
End Effector ◽  
Input And Output ◽  
Planar Manipulators ◽  
Order Polynomial ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Actuated Joints ◽  
Planar Parallel Manipulators

A study of the effect of including a redundant actuated branch on the existence of force-unconstrained configurations for a planar parallel layout of joints is presented1. Two methodologies for finding the force-unconstrained poses are described and discussed. The first method involves the differentiation of the nonlinear kinematic constraints of the input and output variables with respect to time. The second method makes use of the reciprocal screws associated with the actuated joints. The force-unconstrained poses of non-redundantly actuated planar parallel manipulators can be mathematically expressed by means of a polynomial in terms of the three variables that define the dimensional space of the planar manipulator, i.e., the location and orientation of the end-effector. The inclusion of redundant actuated branches leads to a system of polynomials, i.e., one additional polynomial for each redundant branch added. Elimination methods are employed to reduce the number of variables by one for every additional polynomial. This leads to a higher order polynomial with fewer variables. The roots of the resulting polynomial describe the force-unconstrained poses of the manipulator. For planar manipulators it is shown that one order of infinity of force-unconstrained configurations is eliminated for every actuated branch, beyond three, added. As an example, the four-branch revolute-prismatic-revolute mechanism (4-RPR), where the prismatic joints are actuated, is presented.

Type Synthesis of Six-DOF Wrist-Partitioned Parallel Manipulators

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
General Structure ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Forward Displacement ◽  
Serial Manipulators ◽  
Six Dof ◽  
Moving Platform ◽  
Actuated Joints

A six-DOF wrist-partitioned parallel manipulator is a parallel manipulator in which three of the six actuated joints are used to control the position of a point on the moving platform while the other three are further used to control the orientation of the moving platform. Such parallel manipulators are, in fact, the parallel counterparts of the wrist-partitioned serial manipulators, which are widely used in industry. Unlike parallel manipulators of a general structure, a six-DOF wrist-partitioned parallel manipulator usually has simple kinematic characteristics such as its forward displacement analysis and singularity analysis are easy to solve. This paper deals with the type synthesis of six-DOF wrist-partitioned parallel manipulators. An approach is first proposed for the type synthesis of this class of parallel manipulators. Using the proposed approach, six-DOF wrist-partitioned parallel manipulators can be constructed from the types of three-DOF nonoverconstrained spherical parallel manipulators. A large number of six-DOF wrist-partitioned parallel manipulators are then obtained, and several types of practical relevance are also identified.

Type Synthesis of Six-DOF Wrist-Partitioned Fully Parallel Manipulators

2007 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
General Structure ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Forward Displacement ◽  
Serial Manipulators ◽  
Six Dof ◽  
Moving Platform ◽  
Actuated Joints

A six-DOF wrist-partitioned fully parallel manipulator is a parallel manipulator in which three of the six actuated joints are used to control the position of a point on the moving platform while the other three are further used to control the orientation of the moving platform. Such parallel manipulators are in fact the parallel counterparts of the wrist-partitioned serial manipulators, which are widely used in industry. Unlike parallel manipulators of a general structure, a six-DOF wrist-partitioned fully parallel manipulator usually has simple kinematic characteristics such as its forward displacement analysis and singularity analysis are easy to solve. This paper deals with the type synthesis of six-DOF wrist-partitioned fully parallel manipulators. An approach is first proposed for the type synthesis of this class of parallel manipulators. Using the proposed approach, six-DOF wrist-partitioned fully parallel manipulators can be constructed from the types of three-DOF non-overconstrained spherical parallel manipulators. A large number of six-DOF wrist-partitioned fully parallel manipulators are then obtained, and several types of practical relevance are also identified.

Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator

2010 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment Gosselin ◽  
James M. Ritchie
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Actuated Joints ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators — leg actuation singularity — is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.

Inverse Kinematics for Planar Parallel Manipulators

1997 ◽  
Author(s):  
Robert L. Williams ◽  
Brett H. Shelley
Keyword(s):  
Inverse Kinematics ◽  
Broad Class ◽  
Parallel Manipulators ◽  
End Effector ◽  
Serial Chain ◽  
Prismatic Joints ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Serial Chains ◽  
Planar Parallel Manipulators

Abstract This paper presents algebraic inverse position and velocity kinematics solutions for a broad class of three degree-of-freedom planar in-parallel-actuated manipulators. Given an end-effector pose and rate, all active and passive joint values and rates are calculated independently for each serial chain connecting the ground link to the end-effector link. The solutions are independent of joint actuation. Seven serial chains consisting of revolute and prismatic joints are identified and their inverse solutions presented. To reduce computations, inverse Jacobian matrices for overall manipulators are derived to give only actuated joint rates. This matrix yields conditions for invalid actuation schemes. Simulation examples are given.

Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms

1992 ◽  
Vol 114 (3) ◽  
pp. 349-358 ◽  
Author(s):  
V. Kumar
Keyword(s):  
Inverse Kinematics ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Parallel Structure ◽  
End Effector ◽  
Serial Manipulators ◽  
Parallel Scheme ◽  
Parallel Chain ◽  
Manipulation System ◽  
Dual Arm

This paper addresses the instantaneous kinematics of robotic manipulators which have an in-parallel scheme of actuation. Hybrid geometries which require both serial and parallel actuation are also considered. Multifingered grippers, walking vehicles, and multiarm manipulation systems in addition to robot arms with a parallel structure can be included in this broad category. The direct and inverse kinematics (and statics) of these devices is discussed with particular attention to applications in control. An analytical method based on screw system theory for obtaining transformation equations between joint and end-effector coordinates is described. Special configurations in which the end-effector gains or loses a degree of freedom, which are also known as geometric singularities, are an important consideration in this study. This is because the number of special configurations or singularities in the workspace is far more for in-parallel manipulators than that for serial manipulators. The special configurations for a planar dual-arm manipulation system, which can be kinematically modeled as a 5-R linkage, are discussed in some detail as an example.

Jacobian-based stiffness analysis method for parallel manipulators with non-redundant legs

2015 ◽  
Vol 230 (3) ◽  
pp. 341-352 ◽  
Author(s):  
Antonius GL Hoevenaars ◽  
Patrice Lambert ◽  
Just L Herder
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Structural Elements ◽  
Analysis Method ◽  
End Effector ◽  
Stiffness Analysis ◽  
Compliant Joints ◽  
Lower Mobility ◽  
Actuated Joints

Stiffness is an important element in the model of a parallel manipulator. A complete stiffness analysis includes the contributions of joints as well as structural elements. Parallel manipulators potentially include both actuated joints, passive compliant joints, and zero stiffness joints, while a leg may impose constraints on the end-effector in the case of lower mobility parallel manipulators. Additionally, parallel manipulators are often designed to interact with an environment, which means that an external wrench may be applied to the end-effector. This paper presents a Jacobian-based stiffness analysis method, based on screw theory, that effectively considers all above aspects and which also applies to parallel manipulators with non-redundant legs.

scholarly journals A novel three degrees of freedom partially decoupled robot with linear actuators

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 467-475 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Gürsel Alici ◽  
Ramón Rodríguez-Castro
Keyword(s):  
Degrees Of Freedom ◽  
Control Point ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution ◽  
End Effector ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Common Control ◽  
Forward Displacement Analysis

SUMMARYIn this work, a new translational robot formed with two different parallel manipulators with a common control point is introduced. An asymmetric parallel manipulator provides three translational degrees of freedom to the proposed robot while the orientation of the end-effector platform is kept constant by means of a Delta-like manipulator. An exact solution is easily derived to solve the forward displacement analysis while a semi-closed form solution is available for solving the inverse displacement analysis. The infinitesimal kinematics of the robot is approached by applying the theory of screws. Finally, a numerical example that consists of solving the inverse/forward displacement analysis as well as the forward acceleration analysis of the end-effector platform is presented. The example also includes the computation of the workspace and the direct/inverse singularities of the example.

scholarly journals A Dexterity Comparison for 6 DOF Hybrid Robots

2020 ◽  
Author(s):  
MohammadAli Mohammadkhani ◽  
Ahmad Reza Haghighi
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Hybrid Mechanisms ◽  
Six Dof ◽  
Position And Orientation

Abstract In this paper, new hybrid robots are suggested which divided the task into a position and orientation tasks. The position mechanism controls the position whereas the orientation one manipulates the orientation of the end effector. These robots consist of a translational parallel manipulator and a rotational serial or parallel mechanism. The 3UPU or Tricept parallel manipulator and a three-axis gimbaled system or parallel shoulder manipulator are chosen for translational and rotational movements, respectively. The main goal of this paper is analyzing the development and combination of serial and parallel manipulators in order to increase their features. According to this purpose, serial and parallel mechanisms with three DOF are combined in a way to encompass six DOF space. It is shown hybrid mechanisms with less coupling between their subsystems are capable of increasing robot characteristics.

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