Dimensional Synthesis of Planar Six-Bar Linkages by Mechanically Constrain a PRR Serial Chain

2012 ◽  
Author(s):  
Gim Song Soh ◽  
Fangtian Ying ◽  
J. Michael McCarthy
Keyword(s):  
Degree Of Freedom ◽  
Synthesis Process ◽  
Dimensional Synthesis ◽  
Serial Chain ◽  
Prismatic Joints

In this paper, we consider the problem of designing planar six-bar linkages which can be driven by prismatic joints at its base. We explore various ways on how two RR chains can be used to constraint a PRR planar serial chain such that the system yields one-degree of freedom yet passes through a set of five specified task positions. We formulate and solve the design equations as well as analyze the resulting planar six-bar linkage. We demonstrate the synthesis process with the design of the seat of a wheelchair such that it is able to transform itself to be used as a rehabilitation guide during rehabilitation.

Dimensional Synthesis of Planar Eight-Bar Linkages Based on a Parallel Robot With a Prismatic Base Joint

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Fangtian Ying
Keyword(s):  
Rigid Body ◽  
Design Process ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Prismatic Joint ◽  
Serial Chain ◽  
Different Types

This paper details the dimensional synthesis for the rigid body guidance of planar eight-bar linkages that could be driven by a prismatic joint at its base. We show how two RR cranks can be added to a planar parallel robot formed by a PRR and 3R serial chain to guide its end-effector through a set of five task poses. This procedure is useful for designers who require the choice of ground pivot locations. The results are eight different types of one-degree of freedom planar eight-bar linkages. We demonstrate the design process with the design of a multifunctional wheelchair that could transform its structure between a self-propelled wheelchair and a walking guide.

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.

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.

Rigid Body Guidance of Human Gait as Constrained TRS Serial Chain

2014 ◽  
Author(s):  
Gim Song Soh
Keyword(s):  
Degrees Of Freedom ◽  
Point Of View ◽  
Human Gait ◽  
Synthesis Process ◽  
Dimensional Synthesis ◽  
Two Degrees Of Freedom ◽  
Serial Chain ◽  
Optical Motion ◽  
Musculoskeletal Function ◽  
Optical Motion Capture

The motion of gait is a cyclical activity that requires the coordination between locomotion mechanism, motor control and musculoskeletal function. The basic assumption is that one stride is the same as the next. From a simplified kinematics point of view, the human gait can be considered as a TRS serial chain with six degrees-of-freedom driven by the pelvis rotational and tilting motion during walking. This paper presents a dimensional synthesis procedure for the design of two degrees-of-freedom of spatial eight-bar linkages by mechanically constraining a TRS serial chain. The goal is to develop a methodology for the design of under-actuated lower limb walking devices or passively driven exoskeleton systems. The dimensional synthesis process starts with the specification of the links of a TRS chain according to the gait anthropometric data. We show the various ways how four TS constraints can be used to constrain the links of the this chain to obtain a two degrees-of-freedom spatial eight-bar linkage. We formulate and solve the design equations as well as analyze the resulting eight-bar linkage from the data we obtained from an optical motion capture system. An example demonstrates our results.

scholarly journals A New Algorithm for Unique Representation and Isomorphism Detection of Planar Kinematic Chains with Simple and Multiple Joints

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 601
Author(s):  
Mahmoud Helal ◽  
Jong Wan Hu ◽  
Hasan Eleashy
Keyword(s):  
Degree Of Freedom ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Joint Configuration ◽  
Unique Representation ◽  
Kinematic Chains

In this work, a new algorithm is proposed for a unique representation for simple and multiple joint planar kinematic chains (KCs) having any degree of freedom (DOF). This unique representation of KCs enhances the isomorphism detection during the structural synthesis process of KCs. First, a new concept of joint degree is generated for all joints of a given KC based on joint configuration. Then, a unified loop array (ULA) is obtained for each independent loop. Finally, a unified chain matrix (UCM) is established as a unique representation for a KC. Three examples are presented to illustrate the proposed algorithm procedures and to test its validity. The algorithm is applied to get a UCM for planar KCs having 7–10 links. As a result, a complete atlas database is introduced for 7–10-link non-isomorphic KCs with simple or/and multiple joints and their corresponding unified chain matrix.

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.

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.

scholarly journals Design of a Spatial RPR-2SS Valve Mechanism

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Peter L. Wang ◽  
Ulrich Rhem ◽  
J. Michael McCarthy
Keyword(s):  
Tunnel Boring Machine ◽  
Degree Of Freedom ◽  
Valve Mechanism ◽  
Kinematic Synthesis ◽  
Soil Conditioning ◽  
Spatial Mechanism ◽  
Tunnel Boring ◽  
Serial Chain ◽  
Smooth Movement ◽  
Cylindrical Array

This paper applies kinematic synthesis theory to obtain the dimensions of a constrained spatial serial chain for a valve mechanism that cleans and closes a soil conditioning port in a tunnel boring machine. The goal is a smooth movement that rotates a cylindrical array of studs into position and then translates it forward to clean and close the port. The movement of the valve is defined by six positions of the revolute-prismatic-revolute (RPR) serial chain. These six positions are used to compute the dimensions of the two spherical spherical (SS) dyads that constrain the RPR chain to obtain a one degree-of-freedom spatial mechanism. An example design of this valve mechanism is provided in detail.

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.

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