Task Driven Unified Synthesis of Planar Four-Bar and Six-Bar Linkages With Revolute and Prismatic Joints for Five Position Synthesis

2013 ◽  
Author(s):  
Ping Zhao ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Simple Algorithm ◽  
Standing Position ◽  
Type I ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Prismatic Joints ◽  
Seating Position ◽  
Position Synthesis ◽  
The Given ◽  
Synthesis Approach

This paper deals with the problem of integrated joint-type and dimensional synthesis of planar four-bar and six-bar linkages with revolute (R) and prismatic (P) joints for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. The current paper extends this algorithm to the integrated joint-type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages with a combination of R and P joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (Type I), one dyad (Type II), or no dyad (Type III). We demonstrate this task driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

A Task-Driven Unified Synthesis of Planar Four-Bar and Six-Bar Linkages With R- and P-Joints for Five-Position Realization

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Ping Zhao ◽  
Xiangyun Li ◽  
A. Purwar ◽  
Q. J. Ge
Keyword(s):  
Simple Algorithm ◽  
Standing Position ◽  
Type I ◽  
Dimensional Synthesis ◽  
New Classification ◽  
End Effector ◽  
Prismatic Joints ◽  
Seating Position ◽  
The Given ◽  
Synthesis Approach

This paper deals with the problem of integrated joint type and dimensional synthesis of planar four-bar and six-bar linkages, which could contain both revolute (R) and prismatic (P) joints, for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. This paper extends this algorithm to the integrated joint type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages that contain both R- and P-joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (type I), one dyad (type II), or no dyad (type III). In the end, we demonstrate this task-driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

A Fourier Descriptor Approach to Integrated Type and Dimensional Synthesis of Coupled Serial Mechanism for Motion Generation

2019 ◽  
Author(s):  
Hao Lv ◽  
Yuanfei Han ◽  
Xiangyun Li ◽  
Liuxian Zhu
Keyword(s):  
Fourier Descriptor ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Motion Generation ◽  
End Effector ◽  
Novel Approach ◽  
Descriptor Approach ◽  
Harmonic Components ◽  
The Given ◽  
Serial Mechanism

Abstract Coupled serial mechanism is a class of mechanisms that couple the relative rotation of successive links utilizing gears or cable-pulley systems. They can be used to generate complex end-effector trajectories or motions with a single actuator. With the employment of Fourier descriptors, a novel approach to integrate type synthesis and dimensional synthesis of such mechanisms is proposed in this paper. Through the Fourier analysis of two arbitrary trajectories from the given motion, the simplest trajectory that contains the least number of harmonic components is identified. Then, characteristic information of those harmonics such as their numbers, amplitudes and initial phases are used to determine the topology and dimensions of the corresponding coupled serial mechanism, thus effectively solving the motion synthesis problem of this type of mechanisms. Finally, three examples are given to demonstrate the validity of the proposed method.

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.

A non-overconstrained variant of the Agile Eye with a special decoupled kinematics

Robotica ◽  
2013 ◽  
Vol 32 (6) ◽  
pp. 889-905 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai ◽  
Giovanni Legnani
Keyword(s):  
Angular Displacement ◽  
Universal Joint ◽  
Special Configuration ◽  
End Effector ◽  
Revolute Joint ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Decoupled Motion ◽  
Orientation Mechanism ◽  
Actuated Joints

SUMMARYA non-overconstrained three-DOF parallel orientation mechanism that is kinematically equivalent to the Agile Eye is presented in this paper. The output link (end-effector) of the mechanism is connected to the base by one spherical joint and by another three identical legs. Each leg comprises of, in turns from base, a revolute joint, a universal joint, and three prismatic joints. The three lower revolute joints are active joints, while all other joints are passive ones. Based on a special configuration, some three projective angles of the end-effector coordinates are fully decoupled with respect to the input actuated joints, that is, by actuating any revolute joint the end-effector rotates in such a way that the corresponding projective angle changes with the same angular displacement. The fully decoupled motion is analyzed geometrically and proved theoretically. Besides, the inverse and direct kinematics solutions of the mechanism are provided based on the geometric reasoning and theoretical proof.

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

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.

FORCE-UNCONSTRAINED POSES FOR PARALLEL MANIPULATORS WITH REDUNDANT ACTUATED BRANCHES

2005 ◽  
Vol 29 (3) ◽  
pp. 343-356 ◽  
Author(s):  
Flavio Firmani ◽  
Ron P. Podhorodeski
Keyword(s):  
Dimensional Space ◽  
Parallel Manipulators ◽  
End Effector ◽  
Input And Output ◽  
Planar Manipulators ◽  
Order Polynomial ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Actuated Joints ◽  
Planar Parallel Manipulators

A study of the effect of including a redundant actuated branch on the existence of force-unconstrained configurations for a planar parallel layout of joints is presented1. Two methodologies for finding the force-unconstrained poses are described and discussed. The first method involves the differentiation of the nonlinear kinematic constraints of the input and output variables with respect to time. The second method makes use of the reciprocal screws associated with the actuated joints. The force-unconstrained poses of non-redundantly actuated planar parallel manipulators can be mathematically expressed by means of a polynomial in terms of the three variables that define the dimensional space of the planar manipulator, i.e., the location and orientation of the end-effector. The inclusion of redundant actuated branches leads to a system of polynomials, i.e., one additional polynomial for each redundant branch added. Elimination methods are employed to reduce the number of variables by one for every additional polynomial. This leads to a higher order polynomial with fewer variables. The roots of the resulting polynomial describe the force-unconstrained poses of the manipulator. For planar manipulators it is shown that one order of infinity of force-unconstrained configurations is eliminated for every actuated branch, beyond three, added. As an example, the four-branch revolute-prismatic-revolute mechanism (4-RPR), where the prismatic joints are actuated, is presented.

scholarly journals Implementation of a real-time automatic onset time detection for surface electromyography measurement systems using NI myRIO

2016 ◽  
Vol 20 (suppl. 2) ◽  
pp. 591-602 ◽  
Author(s):  
Chaiwat Lersviriyanantakul ◽  
Apidet Booranawong ◽  
Kiattisak Sengchuai ◽  
Pornchai Phukpattaranont ◽  
Booncharoen Wongkittisuksa ◽  
...  
Keyword(s):  
Real Time ◽  
Surface Electromyography ◽  
Onset Time ◽  
Simple Algorithm ◽  
Algorithm Analysis ◽  
The Real ◽  
Measurement Systems ◽  
Smoothing Process ◽  
The Given ◽  
Semg Signals

For using surface electromyography (sEMG) in various applications, the process consists of three parts: an onset time detection for detecting the first point of movement signals, a feature extraction for extracting the signal attribution, and a feature classification for classifying the sEMG signals. The first and the most significant part that influences the accuracy of other parts is the onset time detection, particularly for automatic systems. In this paper, an automatic and simple algorithm for the real-time onset time detection is presented. There are two main processes in the proposed algorithm; a smoothing process for reducing the noise of the measured sEMG signals and an automatic threshold calculation process for determining the onset time. The results from the algorithm analysis demonstrate the performance of the proposed algorithm to detect the sEMG onset time in various smoothing-threshold equations. Our findings reveal that using a simple square integral (SSI) as the smoothing-threshold equation with the given sEMG signals gives the best performance for the onset time detection. Additionally, our proposed algorithm is also implemented on a real hardware platform, namely NI myRIO. Using the real-time simulated sEMG data, the experimental results guarantee that the proposed algorithm can properly detect the onset time in the real-time manner.

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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