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.

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.

Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 232-241 ◽  
Author(s):  
Xichun Nie ◽  
Venkat Krovi
Keyword(s):  
Low Cost ◽  
Synthesis Method ◽  
Path Following ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Serial Chain ◽  
End Effectors ◽  
Serial Chains

Single degree-of-freedom coupled serial chain (SDCSC) mechanisms are a class of mechanisms that can be realized by coupling successive joint rotations of a serial chain linkage, by way of gears or cable-pulley drives. Such mechanisms combine the benefits of single degree-of-freedom design and control with the anthropomorphic workspace of serial chains. Our interest is in creating articulated manipulation-assistive aids based on the SDCSC configuration to work passively in cooperation with the human operator or to serve as a low-cost automation solution. However, as single-degree-of-freedom systems, such SDCSC-configuration manipulators need to be designed specific to a given task. In this paper, we investigate the development of a synthesis scheme, leveraging tools from Fourier analysis and optimization, to permit the end-effectors of such manipulators to closely approximate desired closed planar paths. In particular, we note that the forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. The proposed Fourier-based synthesis method exploits this special structure to achieve the combined number and dimensional synthesis of SDCSC-configuration manipulators for closed-loop planar path-following tasks. Representative examples illustrate the application of this method for tracing candidate square and rectangular paths. Emphasis is also placed on conversion of computational results into physically realizable mechanism designs.

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.

Design of One Degree of Freedom Closed Loop Spatial Chains Using Non-Circular Gears

2009 ◽  
Author(s):  
Mandar Harshe ◽  
Carl Crane ◽  
David B. Dooner
Keyword(s):  
Joint Space ◽  
Optimization Techniques ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Starting Position ◽  
Position Errors ◽  
Spatial Mechanisms ◽  
Error Functional ◽  
Systems Of Polynomial Equations

This paper presents the design of one degree-of-freedom spatial mechanisms that use non-circular gears to constrain the motion. In a spatial body-guidance problem, representing the motion by systems of polynomial equations restricts the number of end-effector positions and orientations (end-effector poses) that can be used as inputs for mechanism design. An approach has been developed that takes any number of desired poses as guide points and develops a mechanism that approximately attains the desired poses over the course of its motion. A problem with implementing this design strategy is the inherent difficulty in accounting for orientation and position errors. The approach described here addresses this problem by defining a new error functional, calculated in the joint space domain. As the mechanisms being dealt with are single degree-of-freedom closed chains, the starting position is a crucial decision in the design process. The method outlines the choice of the starting position and details how this error term can be used along with optimization techniques on either the mechanism parameters or the non-circular gears. A numerical example is presented.

Kinematic and Kinetostatic Synthesis of Planar Coupled Serial Chain Mechanisms

2002 ◽  
Vol 124 (2) ◽  
pp. 301-312 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Solution Approach ◽  
Single Degree ◽  
Design Specifications ◽  
Serial Chain ◽  
Gear Trains ◽  
External Loads

Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms form a novel class of modular and compact mechanisms with a single degree-of-freedom, suitable for a number of manipulation tasks. Such SDCSC mechanisms take advantage of the hardware constraints between the articulations of a serial-chain linkage, created using gear-trains or belt/pulley drives, to guide the end-effector motions and forces. In this paper, we examine the dimensional synthesis of such SDCSC mechanisms to perform desired planar manipulation tasks, taking into account task specifications on both end-effector motions and forces. Our solution approach combines precision point synthesis with optimization to realize optimal mechanisms, which satisfy the design specifications exactly at the selected precision points and approximate them in the least-squares sense elsewhere along a specified trajectory. The designed mechanisms can guide a rigid body through several positions while supporting arbitrarily specified external loads. Furthermore, torsional springs are added at the joints to reduce the overall actuation requirements and to enhance the task performance. Examples from the kinematic and the kinetostatic synthesis of planar SDCSC mechanisms are presented to highlight the benefits.

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.

Formulation of Unique Form of Screw Based Jacobian for Lower Mobility Parallel Manipulators

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Man Bok Hong ◽  
Yong Je Choi
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Unique Form ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Serial Chain ◽  
Velocity Relation ◽  
Lower Mobility ◽  
Serial Chains ◽  
Inverse Velocity

In this paper, the unique form of the screw based Jacobian is suggested for lower mobility parallel manipulators. Utilizing the concept of the reciprocal Jacobian, the forward statics relation for each of the serial kinematic chains of a parallel manipulator can be first obtained and then used to derive both the forward statics and the inverse velocity relations of the manipulator. The screw based Jacobian of a parallel manipulator can be formulated from the inverse velocity relation in such a way that it consists of the reciprocal Jacobians of the serial kinematic chains. Since any reciprocal Jacobian is unique to the corresponding serial chain, the suggested form of the screw based Jacobian is also determined uniquely to the lower mobility parallel manipulator. Two examples are given to illustrate the proposed method, one for the 3DOF parallel manipulator with three identical prismatic-revolute-spherical joints-serial chains and the other for the 4DOF parallel manipulator with nonidentical serial chains (two spherical-prismatic-spherical- and one revolute-revolute-prismatic-revolute joints-serial chains).

scholarly journals Design of a Novel Task-Based Knee Rehabilitation Exoskeleton Device

2018 ◽  
Author(s):  
Visharath Adhikari ◽  
Yimesker Yihun ◽  
Hamid M. Lankarani
Keyword(s):  
Structural Parameters ◽  
Parallel Mechanisms ◽  
Single Degree Of Freedom ◽  
Kinematic Data ◽  
Knee Rehabilitation ◽  
Serial Chain ◽  
Implicit Equations ◽  
Synthesis Procedure ◽  
Serial Chains ◽  
Synthesis Approach

This study is aimed at the design of a novel task-based knee rehabilitation device. The desired trajectories of the knee have been obtained through a vision-based motion capture system. The collected experimental kinematic data has been used as an input to a spatial mechanism synthesis procedure. Parallel mechanisms with single degree-of-freedom (DOF) have been considered to generate the complex 3D motions of the lower leg. An exact workspace synthesis approach is utilized, in which the parameterized forward kinematics equations of each serial chains of the parallel mechanisms are to be converted into implicit equations via elimination. The implicit description of the workspace is made to be a function of the structural parameters of the serial chain, making it easy to relate those parameters to the desired trajectory. The selected mechanism has been verified for the accuracy of its trajectory through CAD modeling and simulations. This design approach reduces alignment and fitting challenges in an exoskeleton as the mechanism does not require alignment of each robotic joint axis with its human counterpart.

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