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.

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.

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.

scholarly journals A Design System for Six-Bar Linkages Integrated With a Solid Modeler

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Kaustubh H. Sonawale ◽  
J. Michael McCarthy
Keyword(s):  
Degree Of Freedom ◽  
Design System ◽  
Solid Model ◽  
Design Algorithm ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Serial Chain ◽  
Tolerance Zones ◽  
Spherical Linkages ◽  
Solid Modeler

This paper presents a design system for planar and spherical six-bar linkages, which is integrated with a solid modeler. The user specifies a backbone 3R chain in five task configurations in the sketch mode of the solid modeler and executes the design system. Two RR constraints are computed, which constrain the 3R chain to a single degree-of-freedom six-bar linkage. There are six ways that these constraints can be added to the 3R serial chain to yield as many as 63 different linkages in case of planar six-bar linkages and 165 in case of spherical six-bar linkages. The performance of each candidate is analyzed, and those that meet the required task are presented to the designer for selection. The design algorithm is run iteratively with random variations applied to the task configurations within user-specified tolerance zones, to increase the number of candidate designs. The output is a solid model of the six-bar linkage. Examples are presented, which demonstrate the effectiveness of this strategy for both planar and spherical linkages.

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.

Seven-Position Synthesis of a Spatial Eight-Bar Linkage by Constraining a TRS Serial Chain

2009 ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Degree Of Freedom ◽  
Upper Arm ◽  
End Effector ◽  
Serial Chain ◽  
Position Synthesis ◽  
Two Degree Of Freedom ◽  
Puma Robot

In this paper, we use seven-position synthesis to add four TS constraints to a TRS serial chain robot and obtain a two degree-of-freedom spatial eight-bar linkage. The TRS chain is an elbow manipulator, similar to a PUMA robot. We synthesize a TS dyad to connect the base of the robot to its forearm, and then we synthesize three TS dyads that connect the upper arm of the robot to its end-effector. The result is a two degree-of-freedom spatial eight-bar linkage that moves through seven prescribed positions. It consists of a TRST loop supporting a 3TS-RS platform, which we denote as a TS-TRS-3TS spatial linkage. We formulate and solve the design equations for the TS dyads, and analyze the resulting eight-bar linkage. An example demonstrates our results.

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.

scholarly journals Synthesis of Spatial RPRP Closed Linkages for a Given Screw System

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Alba Perez-Gracia
Keyword(s):  
Design Method ◽  
Parallel Robots ◽  
Synthesis Problem ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Serial Chain

The dimensional synthesis of spatial chains for a prescribed set of positions can be applied to the design of parallel robots by joining the solutions of each serial chain at the end-effector. This design method does not provide with the knowledge about the trajectory between task positions and, in some cases, may yield a system with negative mobility. These problems can be avoided for some overconstrained but movable linkages if the finite-screw system associated with the motion of the linkage is known. The finite-screw system defining the motion of the robot is generated by a set of screws, which can be related to the set of finite task positions traditionally used in the synthesis theory. The interest of this paper lies in presenting a method to define the whole workspace of the linkage as the input task for the exact dimensional synthesis problem. This method is applied to the spatial RPRP closed linkage, for which one solution exists.

Characterization of Workspaces of Parallel Manipulators

1992 ◽  
Vol 114 (3) ◽  
pp. 368-375 ◽  
Author(s):  
V. Kumar
Keyword(s):  
Parallel Manipulators ◽  
Geometric Optimization ◽  
Reachable Workspace ◽  
Serial Chain ◽  
Kinematic Performance ◽  
Serial Chains ◽  
Manipulator Control ◽  
General Method

The workspaces and kinematic characterization of serial chain manipulator geometries and the geometric optimization have been studied extensively. Much less is known about workspaces for manipulation systems which possess several serial chains arranged in parallel. In this paper, two well known workspaces, the reachable workspace and the dexterous workspace, are investigated for parallel manipulators. A general method for obtaining these workspaces is presented. The existence of numerous special configurations in the workspace present problems in manipulator control. Therefore the controllably dexterous workspace is proposed as a useful measure of kinematic performance. The methodology of delineating the workspaces and its limitations are illustrated with examples.

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.

Development of Path Tracking Control Algorithm for a 4 DOF Spatial Manipulator Using PID Controller

2017 ◽  
pp. 314-327
Author(s):  
Pradeep Reddy Bonikila ◽  
Ravi Kumar Mandava ◽  
Pandu Ranga Vundavilli
Keyword(s):  
Pid Controller ◽  
Dynamic Models ◽  
Control Method ◽  
Robotic Manipulator ◽  
Industrial Applications ◽  
Path Tracking ◽  
End Effector ◽  
Straight Line ◽  
Feedback Control Method ◽  
Manipulator Arm

The path tracking phenomenon of a robotic manipulator arm plays an important role, when the manipulators are used in continuous path industrial applications, such as welding, machining and painting etc. Nowadays, robotic manipulators are extensively used in performing the said tasks in industry. Therefore, it is essential for the manipulator end effector to track the path designed to perform the task in an effective way. In this chapter, an attempt is made to develop a feedback control method for a 4-DOF spatial manipulator to track a path with the help of a PID controller. In order to design the said controller, the kinematic and dynamic models of the robotic manipulator are derived. Further, the concept of inverse kinematics has been used to track different paths, namely a straight line and parabolic paths continuously. The effectiveness of the developed algorithm is tested on a four degree of freedom manipulator arm in simulations.

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