scholarly journals Kinematic Synthesis of Spatial Serial Chains Using Clifford Algebra Exponentials

2006 ◽  
Vol 220 (7) ◽  
pp. 953-968 ◽  
Author(s):  
A Perez-Gracia ◽  
J M McCarthy
Keyword(s):  
Clifford Algebra ◽  
Robotic System ◽  
Exponential Form ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Dual Quaternions ◽  
Serial Chain ◽  
Joint Parameters ◽  
Position And Orientation ◽  
Serial Chains

This article presents a formulation of the design equations for a spatial serial chain that uses the Clifford algebra exponential form of its kinematics equations. This is the even Clifford algebra C+( P3), known as dual quaternions. These equations define the position and orientation of the end effector in terms of rotations or translations about or along the joint axes of the chain. Because the coordinates of these axes appear explicitly, specifying a set of task positions these equations can be solved to determine the location of the joints. At the same time, joint parameters or certain dimensions are specified to ensure that the resulting robotic system has specific features.

Dual Quaternion Synthesis of Constrained Robotic Systems

2003 ◽  
Vol 126 (3) ◽  
pp. 425-435 ◽  
Author(s):  
Alba Perez ◽  
J. M. McCarthy
Keyword(s):  
Parallel Robots ◽  
Robotic Systems ◽  
Dual Quaternion ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Reference Position ◽  
Dual Quaternions ◽  
Design Variables ◽  
Finite Set ◽  
Serial Chains

This paper presents a dual quaternion methodology for the kinematic synthesis of constrained robotic systems. These systems are constructed from one or more serial chains such that each chain imposes at least one constraint on the movement of the workpiece. Serial chains that have constrained workspaces can be synthesized by evaluating the kinematics equations of the chain on a finite set of task positions. In this case, the end-effector positions are known and the Denavit-Hartenberg parameters become design variables. Here we reformulate the kinematics equations in terms of successive screw displacements so the design variables are the coordinates defining the joint axes of the chain in a reference position. Then, dual quaternions defining these transformations are introduced to simplify the structure of the design equations. The result is a synthesis formulation that can be applied to a broad range of constrained serial chains, which can in turn be assembled into constrained parallel robots. We demonstrate the formulation and solution of the dual quaternion design equations for the spatial RPRP chain.

Clifford Algebra Exponentials and Planar Linkage Synthesis Equations

2004 ◽  
Vol 127 (5) ◽  
pp. 931-940 ◽  
Author(s):  
Alba Perez ◽  
J. Michael McCarthy
Keyword(s):  
Clifford Algebra ◽  
Standard Form ◽  
Algebraic Manipulation ◽  
Algebraic Solution ◽  
Linkage Design ◽  
Serial Chain ◽  
The Matrix ◽  
Basic Equations ◽  
Serial Chains ◽  
Linkage Synthesis

This paper uses the exponential defined on a Clifford algebra of planar projective space to show that the “standard-form” design equations used for planar linkage synthesis are obtained directly from the relative kinematics equations of the chain. The relative kinematics equations of a serial chain appear in the matrix exponential formulation of the kinematics equations for a robot. We show that formulating these same equations using a Clifford algebra yields design equations that include the joint variables in a way that is convenient for algebraic manipulation. The result is a single formulation that yields the design equations for planar 2R dyads, 3R triads, and nR single degree-of-freedom coupled serial chains and facilitates the algebraic solution of these equations including the inverse kinematics of the chain. These results link the basic equations of planar linkage design to standard techniques in robotics.

Kinematic Synthesis of Spatial R-R Dyads for Path Following Revisited Using the Rotation Matrix Approach

1999 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Linear System ◽  
Path Following ◽  
Rotation Matrix ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Serial Chain ◽  
Systematic Development ◽  
Matrix Vector ◽  
Selection Of

Abstract We revisit the dimensional synthesis of a spatial two-link, two revolute-jointed serial chain for path following applications, focussing on the systematic development of the design equations and their analytic solution for the three precision point synthesis problem. The kinematic design equations are obtained from the equations of loop-closure for end-effector position in rotation-matrix/vector form at the three precision points. These design equations form a rank-deficient linear system in the link-vector components. The nullspace of the rank deficient linear system is then deduced analytically and interpreted geometrically. Tools from linear algebra are applied to systematically create the auxiliary conditions required for synthesis and to verify consistency. An analytic procedure for obtaining the link-vector components is then developed after a suitable selection of free choices. Optimization over the free choices is possible to permit the matching of additional criteria and explored further. Examples of the design of optimal two-link coupled spatial R-R dyads are presented where the end-effector interpolates three positions exactly and closely approximates an entire desired path.

scholarly journals A Design System for Eight-Bar Linkages as Constrained 4R Serial Chains

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kaustubh H. Sonawale ◽  
J. Michael McCarthy
Keyword(s):  
Random Search ◽  
Design System ◽  
End Effector ◽  
Serial Chain ◽  
Straight Line ◽  
Tolerance Zones ◽  
Serial Chains

This paper presents a design system for planar eight-bar linkages that adds three RR constraints to a user-specified 4R serial chain. R denotes a revolute, or hinged, joint. There are 100 ways in which these constraints can be added to yield as many as 3951 different linkages. An analysis routine based on the Dixon determinant evaluates the performance of each linkage candidate and determines the feasible designs that reach the task positions in a single assembly. A random search within the user-specified tolerance zones around the task specifications is iterated in order to increase the number of linkage candidates and feasible designs. The methodology is demonstrated with the design of rectilinear eight-bar linkages that guide an end-effector through five parallel positions along a straight line.

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.

Workspace and Singularity Characteristics of 3-DOF Planar Parallel Robots

2009 ◽  
Author(s):  
Ming Huang
Keyword(s):  
Computer Simulations ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Geometric Parameters ◽  
Kinematic Structure ◽  
Link Length ◽  
End Effector ◽  
Serial Chain ◽  
Parametric Studies ◽  
Position And Orientation

A study of workspace and singularity characteristics is presented for two common types of 3-DOF planar parallel robot manipulators. The robots considered feature a kinematic structure with 3 in-parallel actuated, R-R-R and R-P-R serial chain geometries. In this study, computer simulations aided with graphic visualization were used to characterize the complete pose workspace (for ranges of both position and orientation) and the singularity inherent to the systems. Parametric studies have also been performed to ascertain the way in which both characteristics vary with respect to various geometric parameters such as pivot location, link length, and platform size for end-effector. Results are shown by way of a unique composite ratio of the available workspace to the density of singularity within that workspace.

Vision- based control of a mobile manipulator with an adaptable-passive suspension for unstructured environments

2021 ◽  
pp. 1-38
Author(s):  
Antonio Cardenas ◽  
Osmar Quiroz ◽  
Ricardo Hernandez ◽  
Hugo I. Medellin-Castillo ◽  
Alejandro González ◽  
...  
Keyword(s):  
Mobile Robot ◽  
Experimental Validation ◽  
Experimental Tests ◽  
Mobile Manipulator ◽  
Robotic Platform ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Uneven Terrain ◽  
Passive Mechanism ◽  
Position And Orientation

Abstract The kinematic design and navigation control of a new autonomous mobile manipulator for uneven terrain is presented in this work. An innovative suspension system's design is based on the kinematic synthesis of an adaptable, passive mechanism that compensates for irregularities in the terrain and facilitate the control of the robotic platform using cameras. The proposed mobile robot suspension consists of two pairs of bogies joined by a crank-slider mechanism that allows the robot to adapt to the terrain irregularities. The mobile robot is also equipped with a robotic manipulator, of which a synthesis, simulation, and experimental validation are presented while manipulation is accomplished during movements on rough terrain. The proposed mobile robot has been fabricated using additive manufacturing (AM) techniques. A linear camera space manipulation (LCSM) control system has been developed and implemented to conduct experimental tests along uneven terrain. This mobile manipulator has been designed to transverse uneven terrain so that the loading platform is kept horizontal while crossing obstacles up to one-third of the size of its wheels. This feature allows the onboard cameras to stay oriented towards the target. The vision-based paradigm that enables the control of this mobile manipulator allows to estimate the position and orientation of its end effector and update the trajectory of the manipulator along the path towards the target. The experiments show a final precision for engagement of a pallet within +/− 2.5 mm in position and +/− 2 degrees in orientation.

scholarly journals Synthesis of an NR Robot With Four-Bar Constraining Modules

2014 ◽  
Author(s):  
Brandon Y. Tsuge ◽  
J. Michael McCarthy
Keyword(s):  
General Procedure ◽  
Robotic System ◽  
End Effector ◽  
Serial Chain ◽  
Path Synthesis ◽  
Four Bar Linkage

This paper uses coupler-path synthesis to design four-bar linkage modules that constrains the movement of links in an nR serial chain. The goal is to formulate a general procedure for path-synthesis of a robotic system using four-bar linkages. A desired end-effector trajectory is transformed into a secondary trajectory that is used for nine-point synthesis of a constraining four-bar linkage. This procedure constrains an nR chain to become a 4n-2 bar linkage. An example presents the constraint of a 2R chain to a six-bar that has a prescribed trajectory for an end-effector point.

Dimensional Synthesis of CRR Serial Chains

2003 ◽  
Author(s):  
Alba Perez ◽  
J. M. McCarthy
Keyword(s):  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Dual Quaternion ◽  
Kinematic Synthesis ◽  
Revolute Joints ◽  
Serial Chain ◽  
In Series ◽  
Synthesis Methodology ◽  
Serial Chains

This paper presents the kinematic synthesis of a CRR serial chain. This is a four-degree-of-freedom chain constructed from a cylindric joint and two revolute joints in series. The design equations for this chain are obtained from the dual quaternion kinematics equations evaluated at a specified set of task positions. In this case, we find that the chain is completely defined by seven task positions. Furthermore, our solution of these equations has yielded 52 candidate designs, so far; there may be more. This synthesis methodology shows promise for the design of constrained serial chains.

Synthesis of Spatial Two-Link Coupled Serial Chains

1998 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Path Following ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Serial Chain ◽  
Serial Chains ◽  
Selection Of

Abstract We address the synthesis of serial chain spatial mechanisms with revolute joints in which the rotations about the joints are coupled via cables and pulleys. Such coupled serial chain mechanisms offer a middle ground between the more versatile and compact serial chains and the simpler closed chains by combining some of the advantages of both types of systems. In particular, we focus on the synthesis of single degree-of-freedom, coupled serial chains with two revolute joints. We derive precision point synthesis equations for two precision points by combining the loop closure equations with the necessary geometric constraints in terms of the unknown mechanism parameters. This system of equations can now be solved linearly for the link vectors after a suitable selection of free choices. We optimize over the free choices to generate an end effector trajectory that closely approximates a desired end effector trajectory for motion generation and path following applications.

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