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.

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.

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.

Synthesis of Planar RR Dyads by Constraint Manifold Projection

1996 ◽  
Author(s):  
Pierre M. Larochelle
Keyword(s):  
Rigid Body ◽  
Design Methodology ◽  
Analytical Representation ◽  
Dimensional Synthesis ◽  
Constraint Manifold ◽  
Design Case ◽  
Design Case Study

Abstract In this paper we present the constraint manifold of the planar RR dyad. The constraint manifold is an analytical representation of the workspace of the dyad. We then derive a technique, utilizing the constraint manifold, for performing the dimensional synthesis of planar RR dyads for approximate rigid body guidance through n positions. Finally, we present the implementation of the design methodology in the software VISSYN and discuss its use in a design case study.

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.

scholarly journals Hybrid Optimization Based Mathematical Procedure for Dimensional Synthesis of Slider-Crank Linkage

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1581
Author(s):  
Alfonso Hernández ◽  
Aitor Muñoyerro ◽  
Mónica Urízar ◽  
Enrique Amezua
Keyword(s):  
Genetic Algorithm ◽  
Fitness Function ◽  
Linear Equations ◽  
Optimization Procedure ◽  
Optimization Techniques ◽  
Dimensional Synthesis ◽  
Hybrid Strategy ◽  
Dimensional Parameters ◽  
Optimization Methodology ◽  
Crank Mechanism

In this paper, an optimization procedure for path generation synthesis of the slider-crank mechanism will be presented. The proposed approach is based on a hybrid strategy, mixing local and global optimization techniques. Regarding the local optimization scheme, based on the null gradient condition, a novel methodology to solve the resulting non-linear equations is developed. The solving procedure consists of decoupling two subsystems of equations which can be solved separately and following an iterative process. In relation to the global technique, a multi-start method based on a genetic algorithm is implemented. The fitness function incorporated in the genetic algorithm will take as arguments the set of dimensional parameters of the slider-crank mechanism. Several illustrative examples will prove the validity of the proposed optimization methodology, in some cases achieving an even better result compared to mechanisms with a higher number of dimensional parameters, such as the four-bar mechanism or the Watt’s mechanism.

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.

Design of a Two-Input Linkage-Based Motor

1996 ◽  
Author(s):  
Yassir Shanshal ◽  
Kambiz Farhang
Keyword(s):  
Design Methodology ◽  
Angular Motion ◽  
Dimensional Synthesis ◽  
Reciprocating Motion ◽  
Linkage Mechanism ◽  
Motion Synthesis ◽  
Small Motion ◽  
Motor Design ◽  
Input Motion ◽  
Approximate Equations

Abstract This paper proposes the use of a seven-bar linkage mechanism to obtain a multiply actuated motor. Design of two input mechanisms is presented involving two synthesis sub-tasks of input motion synthesis and dimensional synthesis. To this end a design methodology is presented based on the theory of small crank mechanisms. For the case of small motion, approximate equations are developed with the premise that as a result of small reciprocating motion of the input actuators, the motion of every link, with the exception of the output, is small. The motion, in turn, is expressed as a sum of an average and a small oscillatory angular motion about the average. A set of design equations are obtained from the approximate kinematic equations. The design methodology is exemplified using the synthesis of a seven-link mechanism with two translating inputs.

Determination of the Interference Distance Between Two Objects Using Optimization Techniques

1994 ◽  
Author(s):  
Meyer Nahon
Keyword(s):  
Optimization Problem ◽  
Accurate Determination ◽  
Separation Distance ◽  
Optimization Techniques ◽  
Robotic Systems ◽  
Separation Problem ◽  
Optimization Formulation ◽  
Minimum Separation ◽  
Two Bodies

Abstract The determination of the interference distance between objects is a problem encountered in the off-line simulation of robotic systems. It is similar to the problem of finding the minimum separation distance between two bodies — a problem which, at present, is commonly solved using optimization techniques. This paper presents an analogous optimization formulation for the quick and accurate determination of the interference distance between two interfering objects. The optimization problem consists of finding the maximum amount by which the boundaries of two interfering object can be moved back while still maintaining a non-empty interference volume. Since the approach used is similar to that used in the minimum separation problem, a single algorithm has been implemented which, given the position and orientation of two objects, will return the separation or interference distance between the objects, as appropriate.

Dimensional Synthesis and Constrained Motion Interpolation for Planar and Spherical 6R Closed Chains

2008 ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Qiaode Jeffrey Ge
Keyword(s):  
Rational Curve ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Initial Attempt ◽  
Kinematic Constraints ◽  
Constraint Manifold ◽  
Cartesian Space ◽  
Closed Chain ◽  
Kinematic Mapping ◽  
The Given

In the recent past, we have studied the problem of synthesizing rational interpolating motions under the kinematic constraints of any given planar and spherical 6R closed chain. This work presents some preliminary results on our initial attempt to solve the inverse problem, that is to determine the link lengths of planar and spherical 6R closed chains that follow a given smooth piecewise rational motion under the kinematic constraints. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of planar and spherical closed chains in the Cartesian space. By using kinematic mapping and a quaternions based approach to represent displacements of the coupler of the closed chains, the given smooth piecewise rational motion is mapped to a smooth piecewise rational curve in the space of quaternions. In this space, the aforementioned workspace constraints on the coupler of the closed chains define a constraint manifold representing all the positions available to the coupler. Thus the problem of dimensional synthesis may be solved by modifying the size, shape and location of the constraint manifolds such that the mapped rational curve is contained entirely inside the constraint manifolds. In this paper, two simple examples with preselected moving pivots on the coupler as well as fixed pivots are presented to illustrate the feasibility of this approach.

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