Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Positions

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Pick And Place ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyad's rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed positions to yield designs that exactly reach the prescribed pick and place positions while approximating an arbitrary number of guiding positions. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain, also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on elements of SE(2); the group of planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. Two examples that demonstrate the synthesis technique are included.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Locations

2013 ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyads rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed locations to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain; also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. An example that demonstrates the synthesis technique is included.

Synthesis of Watt II Mechanisms for Four Simultaneous Positions

2015 ◽  
Author(s):  
Pierre Larochelle ◽  
Jugesh Sundram ◽  
Ronald A. Zimmerman
Keyword(s):  
Algebraic Geometry ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Generation Task ◽  
Kinematic Synthesis ◽  
Synthesis Algorithm ◽  
Relative Angle ◽  
Synthesis Technique ◽  
Two Bodies

This article presents the kinematic synthesis of Watt II six-bar mechanisms for simultaneously guiding two bodies through four prescribed positions. The two bodies to be moved are connected by a revolute joint and the motion generation task is defined by the four desired positions of one body and the relative angle of the second body with respect to the first body. The methodology uses an algebraic geometry formulation of the exact synthesis of planar RR dyads for four prescribed positions from classical Burmester theory. The result is a dimensional synthesis technique for designing Watt II mechanisms for four simultaneous positions. A case study illustrating the application of the synthesis algorithm is included.

Approximate Motion Synthesis of Open and Closed Chains via Parametric Constraint Manifold Fitting: Preliminary Results

2003 ◽  
Author(s):  
Pierre M. Larochelle
Keyword(s):  
Optimization Techniques ◽  
Robotic Systems ◽  
Dimensional Synthesis ◽  
Motion Synthesis ◽  
Open Chain ◽  
Constraint Manifold ◽  
Synthesis Technique ◽  
Numerical Design ◽  
Design Case ◽  
Parametric Constraint

In this paper we present a novel dyad dimensional synthesis technique for approximate motion synthesis. The methodology utilizes an analytic representation of the dyad’s constraint manifold that is parameterized by its dimensional synthesis variables. Nonlinear optimization techniques are then employed to minimize the distance from the dyad’s constraint manifold to a finite number of desired locations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to planar, spherical, and spatial dyads. Here, we specifically address the planar RR, spherical RR and spatial CC dyads since these are often found in the kinematic structure of robotic systems and mechanisms. These dyads may be combined serially to form a complex open chain (e.g. a robot) or when connected back to the fixed link they may be joined so as to form one or more closed chains (e.g. a linkage, a parallel mechanism, or a platform). Finally, we present some initial numerical design case studies that demonstrate the utility of the synthesis technique.

Approximate Motion Synthesis of Spherical Kinematic Chains

2007 ◽  
Author(s):  
Venkatesh Venkataramanujam ◽  
Pierre Larochelle
Keyword(s):  
Finite Number ◽  
Nonlinear Optimization ◽  
Optimization Technique ◽  
Analytic Representation ◽  
Dimensional Synthesis ◽  
Motion Synthesis ◽  
Kinematic Chains ◽  
Synthesis Technique

In this paper we present a novel dimensional synthesis technique for approximate motion synthesis of spherical kinematic chains. The methodology uses an analytic representation of the spherical RR dyad’s workspace that is parameterized by its dimensional synthesis variables. A two loop nonlinear optimization technique is then employed to minimize the distance from the dyad’s workspace to a finite number of desired orientations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to spherical open and closed kinematic chains. Here, we specifically address the spherical RR open and 4R closed chains however the methodology is applicable to all spherical kinematic chains. Finally, we present two examples that demonstrate the utility of the synthesis technique.

A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Q. J. Ge ◽  
Feng Gao
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Geometric Framework ◽  
Kinematic Chains ◽  
Kinematic Mapping ◽  
Spherical Linkages ◽  
Spatial Displacements ◽  
The Given

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

MotionGen: Interactive Design and Editing of Planar Four-Bar Motions for Generating Pose and Geometric Constraints

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Anurag Purwar ◽  
Shrinath Deshpande ◽  
Q. J. Ge
Keyword(s):  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Unified Framework ◽  
Synthesis Algorithm ◽  
Approximate Synthesis ◽  
High Utility ◽  
High Level ◽  
Generation Problem ◽  
Practical Constraints

In this paper, we have presented a unified framework for generating planar four-bar motions for a combination of poses and practical geometric constraints and its implementation in MotionGen app for Apple's iOS and Google's Android platforms. The framework is based on a unified type- and dimensional-synthesis algorithm for planar four-bar linkages for the motion-generation problem. Simplicity, high-utility, and wide-spread adoption of planar four-bar linkages have made them one of the most studied topics in kinematics leading to development of algorithms and theories that deal with path, function, and motion generation problems. Yet to date, there have been no attempts to develop efficient computational algorithms amenable to real-time computation of both type and dimensions of planar four-bar mechanisms for a given motion. MotionGen solves this problem in an intuitive fashion while providing high-level, rich options to enforce practical constraints. It is done effectively by extracting the geometric constraints of a given motion to provide the best dyad types as well as dimensions of a total of up to six four-bar linkages. The unified framework also admits a plurality of practical geometric constraints, such as imposition of fixed and moving pivot and line locations along with mixed exact and approximate synthesis scenarios.

Design, Synthesis and Experiment of Foot-driven Lower Limb Rehabilitation Mechanisms

2021 ◽  
pp. 1-44
Author(s):  
Chennan Yu ◽  
Jun Ye ◽  
Jiangming Jia ◽  
Xiong Zhao ◽  
Zhiwei Chen ◽  
...  
Keyword(s):  
Ankle Joint ◽  
Lower Limb ◽  
Gear Train ◽  
Home Healthcare ◽  
Dimensional Synthesis ◽  
Linkage Mechanism ◽  
Open Chain ◽  
Rehabilitation Training ◽  
Limb Rehabilitation ◽  
Lower Limb Rehabilitation

Abstract A foot-driven rehabilitation mechanism is suitable for home healthcare due to its advantages of simplicity, effectiveness, small size, and low price. However, most of the existing studies on lower limb rehabilitation movement only consider the trajectory of the ankle joint and ignore the influence of its posture angle, which makes it difficult to ensure the rotation requirements of the ankle joint and achieve a better rehabilitation effect. Aiming at the shortcomings of the current research, this paper proposes a new single degree-of-freedom (DOF) configuration that uses a noncircular gear train to constrain the three revolute joints (3R) open-chain linkage and expounds its dimensional synthesis method. Then, a parameter optimization model of the mechanism is established, and the genetic algorithm is used to optimize the mechanism parameters. According to the eight groups of key poses and position points of the ankle joint and the toe, the different configurations of the rehabilitation mechanism are synthesized and compared, and it is concluded that the newly proposed 3R open-chain noncircular gear-linkage mechanism exhibits better performance. Finally, combined with the requirements of rehabilitation training, a lower limb rehabilitation training device is designed based on this new configuration, and a prototype is developed and tested. The test results show that the device can meet the requirements of the key position points and posture angles of the ankle joint and the toe and verify the correctness of the proposed dimensional synthesis and optimization methods.

A Synthesis Algorithm of Three-Revolute Manipulators by Means of the Workspace Contour Algebraic Formulation

1992 ◽  
Author(s):  
Marco Ceccarelli
Keyword(s):  
Multiple Solutions ◽  
Algebraic Form ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Algebraic Formulation

Abstract A synthesis algorithm of general three-revolute open chain manipulators is proposed making use of an algebraic formulation of the workspace contour, which has been deduced in a previous paper. The algebraic form of the synthesis model allows to formulate some algebraic design equations and to discuss the number and the type of the multiple solutions.

Dimensional Synthesis of a Novel 2T2R Parallel Manipulator for Medical Applications

2014 ◽  
Author(s):  
Nitish Kumar ◽  
Olivier Piccin ◽  
Bernard Bayle
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Structural Parameters ◽  
Geometric Analysis ◽  
Medical Applications ◽  
Dimensional Synthesis ◽  
Synthesis Algorithm ◽  
Percutaneous Procedures ◽  
Actuated Joints

This paper deals with the dimensional synthesis of a novel parallel manipulator for medical applications. This parallel mechanism has a novel 2T2R mobility derived from the targeted application of needle manipulation. The kinematic design of this 2T2R manipulator and its novelty are illustrated in relation to the percutaneous procedures. Due to the demanding constraints on its size and compactness, achieving a large workspace especially in orientation, is a rather difficult task. The workspace size and kinematic constraint analysis are considered for the dimensional synthesis of this 2T2R parallel mechanism. A dimensional synthesis algorithm based on the screw theory and the geometric analysis of the singularities is described. This algorithm also helps to eliminate the existence of voids inside the workspace. The selection of the actuated joints is validated. Finally, the dimensions of the structural parameters of the mechanism are calculated for achieving the required workspace within the design constraints of size, compactness and a preliminary prototype without actuators is presented.

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