scholarly journals Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 72 ◽  
Author(s):  
Stefan Schulz
Keyword(s):  
Lower Bound ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Parallel Mechanisms ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Measurement Units ◽  
Linear Actuators ◽  
Direct Kinematics

In this paper, we experimentally evaluate the performance of a sensor concept for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism by using solely the linear actuators’ orientations. At first, we review classical methods for solving the direct kinematics problem of parallel mechanisms and discuss their disadvantages on the example of the general planar 3-RPR parallel mechanism, a planar parallel robot with two translational and one rotational degrees of freedom, where P denotes active prismatic joints and R denotes passive revolute joints. In order to avoid these disadvantages, we present a sensor concept together with an analytical formulation for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism where the number of possible assembly modes can be significantly reduced when the linear actuators’ orientations are used instead of their lengths. By measuring the orientations of the linear actuators, provided, for example, by inertial measurement units, only two assembly modes exist. Finally, we investigate the accuracy of our direct kinematics solution under static as well as dynamic conditions by performing experiments on a specially designed prototype. We also investigate the solution formulation’s amplification of measurement noise on the calculated pose and show that the Cramér-Rao lower bound can be used to estimate the lower bound of the expected variances for a specific pose based exclusively on the variances of the linear actuators’ orientations.

scholarly journals On Using Inertial Measurement Units for Solving the Direct Kinematics Problem of Parallel Mechanisms

Robotics ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 99
Author(s):  
Stefan Schulz
Keyword(s):  
Low Cost ◽  
Parallel Mechanisms ◽  
Inertial Measurement Units ◽  
Inertial Measurement ◽  
Sensor Structure ◽  
Prismatic Joints ◽  
Measurement Units ◽  
Linear Actuators ◽  
Achievable Accuracy ◽  
Direct Kinematics

In this paper, we investigate the accuracy and the computational efficiency of an IMU-based approach for solving the direct kinematics problem of parallel mechanisms with length-variable linear actuators under dynamic conditions. By avoiding to measure the linear actuators’ lengths and by using orientations instead, a comprehensive, low-cost sensor structure can be obtained that provides a unique solution for the direct kinematics problem. As a representative example, we apply our approach to the planar 3-RPR parallel mechanism, where P denotes active prismatic joints and R denotes passive revolute joints, and investigate the achievable accuracy and robustness on a specially designed experimental device. In this context, we also investigate the effect of sensor fusion on the achievable accuracy and compare our results with those obtained from linear actuators’ lengths when the Newton-Raphson algorithm is used to compute the manipulator platform’s pose iteratively. Finally, we discuss the applicability of inertial measurement units (IMUs) for solving the direct kinematics problem of parallel mechanisms.

A New Family of 4-DOF Parallel Mechanisms (1T-3R and 2T-2R) With Two Platforms and Its Application to a Footpad Device

2004 ◽  
Author(s):  
Jungwon Yoon ◽  
Jeha Ryu
Keyword(s):  
Degrees Of Freedom ◽  
Base Plate ◽  
Driving Mechanism ◽  
Parallel Mechanisms ◽  
Pitch Motion ◽  
Human Foot ◽  
New Family ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Kinematic Analyses

This paper proposes a new family of four degrees-of-freedom (dof) parallel mechanisms with two platforms and its application to a footpad device that can simulate the spatial motions of the human foot. The new mechanism consists of front and rear platforms, and three limbs. Two limbs with 6-dof serial joints (P-S-P-P) are attached to each platform and are perpendicular to the base plate, while the middle limb (Pe-Re-R or Pe-Pe-R) is attached to the revolute joint that connects the front and rear platforms. The middle limb is driven by the 2-dof driving mechanism that is equivalent active serial prismatic and revolute joints (Pe-Re), or prismatic and prismatic joints (Pe-Re) with two base-fixed prismatic actuators. Therefore, two new 4-dof parallel mechanisms with two platforms can generate pitch motion of each platform, and roll and heave motions (1T-3R) or pitch motion of each platform and two translational motions (2T-2R) at both platforms. Kinematic analyses of the 1T-3R mechanism were performed, including inverse and forward kinematics, and velocity analysis. Based on the 1T-3R mechanism, a footpad device was designed to generate foot trajectories for natural walking. Finally, simulations of the foot trajectories in the normal gait cycle were performed using the proposed footpad device.

scholarly journals Repeatability Analysis of Overconstrained Kinematic Coupling Using a Parallel-Mechanism-Equivalent Model

2020 ◽  
Author(s):  
Jianzhong Ding ◽  
Xueao Liu ◽  
chunjie wang
Keyword(s):  
Parallel Mechanism ◽  
Sampling Method ◽  
Contact Forces ◽  
Equivalent Model ◽  
Parallel Mechanisms ◽  
Kinematic Coupling ◽  
Contact Points ◽  
Prismatic Joints ◽  
Type Coupling ◽  
Additional Support

Abstract A novel method for repeatability analysis of overconstrained kinematic coupling using a parallel-mechanism-equivalent-model is proposed. An overconstrained Kelvin-type coupling with one additional support is introduced and used for method illustration. Contact forces of the overconstrained coupling under preload are computed with Moore-Penrose inverse and the deformations are obtained using the Hertz theory. The couping is equivalently modeled as a 7-SPS parallel mechanism, spherical joints of which represent the centers of the supporting balls and the contact points, respectively, and prismatic joints are used to simulate the deformations. Therefore, pose error of the coupling arisen from preload is analyzed using the well-appraised incremental method for forward kinematics analysis of parallel mechanisms. The uncertainties of the preload are discussed and a boundary-sampling method is proposed for repeatability analysis. The main contribution of this study lies in that the proposed parallel-mechanism-equivalent-model and the boundary-sampling method greatly simplify the repeatability analysis of overconstrained kinematic couplings. Finally, the proposed methods are validated by case study.

Design of a Four Legged Parallel Mechanism to Improve the Dexterity of Walking Robot

2009 ◽  
Author(s):  
ChiHyo Kim ◽  
KunWoo Park ◽  
TaeSung Kim ◽  
MinKi Lee
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Topology Design ◽  
Condition Numbers ◽  
Walking Robots ◽  
Rough Terrain ◽  
Parallel Mechanisms ◽  
Walking Robot ◽  
Intermediate Mechanism

This paper designs a four legged parallel mechanism to improve the dexterity of three layered parallel walking robot. Topology design is conducted for a leg mechanism composed of four legs, base and ground, which constitute a redundant parallel mechanism. This mechanism is subdivided into four sub-mechanism composed of three legs. A motor vector is adopted to determine the 6×8 Jacobian of the redundant parallel mechanism and the 6×6 Jacobian of the sub-mechanisms, respectively. The condition number of the Jacobian matrix is used as an index to measure a dexterity. We analyze the condition numbers of the Jacobian over the positional and orientational walking space. The analytical results show that a sub-mechanism has lots of singularities within workspace but they are removed by a redundant parallel mechanism improving the dexterity. This paper presents a parallel typed walking robot to enlarge walking space and stability region. Seven types of three layered walking robots are designed by inserting an intermediate mechanism between the upper and the lower legged parallel mechanisms. They provide various types of gaits to walk rough terrain and climb over a wall with small degrees of freedom.

scholarly journals Reconfiguration Analysis of a 3-DOF Parallel Mechanism

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
The Third ◽  
Equilateral Triangles ◽  
Moving Platform

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

Kinematics and Workspace Analysis of 3-RPP Parallel Mechanism

2013 ◽  
Vol 456 ◽  
pp. 146-150
Author(s):  
Zhi Jiang Xie ◽  
Jun Zhang ◽  
Xiao Bo Liu
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Parallel Mechanisms ◽  
Vector Method ◽  
Workspace Analysis ◽  
Inverse Solutions ◽  
Three Degrees Of Freedom

This paper designed a kind of parallel mechanism with three degrees of freedom, the freedom and movement types of the robot are analyzed in detail, the parallel mechanisms Kinematics positive and inverse solutions are derived through using the vector method. And at last its workspace is analyzed and studied systematically.

Redundant Parallel Mechanism for Haptic Applications

2010 ◽  
Vol 4 (4) ◽  
pp. 338-345 ◽  
Author(s):  
Jumpei Arata ◽  
◽  
Hideo Fujimoto
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Display Device ◽  
Parallel Mechanisms ◽  
Prototype Implementation ◽  
Haptic Devices ◽  
Multiple Degrees Of Freedom ◽  
High Rigidity ◽  
Wide Range ◽  
Fixed Base

With haptic devices becoming increasingly common in both industrial field and consumer use, parallel mechanisms have been widely introduced for their high rigidity, output, accuracy and high backdrivability due to their multi-legged structure and fixed base actuators. In general parallel mechanism, redundancy enlarges the working area and avoids singularity. The redundant parallel mechanism we present introduces these advantages into haptic applications. Introducing this mechanism into a multiple degrees-of-freedom (DOF) structure realizes a wide range of working areas in rotation. The redundant parallel mechanism implemented in translational force display device, and multi-DOF force display device demonstrate the advantages of the redundant parallel mechanism in haptic applications. Following an overview, we introduce the prototype implementation and evaluation of these devices and discuss the effectiveness of the redundant parallel mechanism in haptic applications.

scholarly journals A Translational Three-Degrees-of-Freedom Parallel Mechanism With Partial Motion Decoupling and Analytic Direct Kinematics

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Huiping Shen ◽  
Damien Chablat ◽  
Boxiong Zeng ◽  
Ju Li ◽  
Guanglei Wu ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Design Theory ◽  
Degrees Of Freedom ◽  
Analytic Solutions ◽  
Inverse Kinematic ◽  
Kinematic Modeling ◽  
Topological Design ◽  
Prismatic Joints ◽  
Topological Characteristics ◽  
Three Degrees Of Freedom

Abstract According to the topological design theory and the method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, this paper studied a three-degrees-of-freedom (3-DOF) translational PM that has three advantages, i.e., (i) it consists of three fixed actuated prismatic joints, (ii) the PM has analytic solutions to the direct and inverse kinematic problems, and (iii) the PM is of partial motion decoupling property. First, the main topological characteristics, such as the POC, degree-of-freedom, and coupling degree, were calculated for kinematic modeling. Thanks to these properties, the direct and inverse kinematic problems can be readily solved. Further, the conditions of the singular configurations of the PM were analyzed, which corresponds to its partial motion decoupling property.

scholarly journals Simulation of a parallel mechanical elbow with 3 DOF

2009 ◽  
Vol 7 (02) ◽  
Author(s):  
J. R. Mendoza-Vázquez ◽  
E. Tlelo-Cuautle ◽  
J.L. Vázquez-Gonzalez ◽  
A. Z. Escudero-Uribe
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Mechanical Support ◽  
Simulation And Modeling ◽  
Matlab Simulation ◽  
Geometric Methods ◽  
Kinematics Simulation ◽  
Linear Actuators ◽  
Simulation Results

The kinematics simulation and modeling of a mechanical elbow of 3 degrees of freedom, is introduced by highlighting the main features of the mechanism related to the design criteria. The mechanical elbow is used as a transhumeral prosthetic part, and it has been built as a parallel topology consisting of electric linear actuators and universal joints. The parallel mechanism has 4 legs. 3 are electric linear actuators, and the fourth leg provides mechanical support for the whole structure and holds a DC Motor that performs the action of gripping objects. Furthermore, this paper shows the inverse kinematics for the elbow by geometric methods, and the MatLab‐simulation results show the workspace of the movement and the ability of the mechanical elbow to replicate the movements of a biological one.

scholarly journals Design and Kinematic Analysis of a Novel 2-DoF Closed-Loop Mechanism for the Actuation of Machining Robots

2021 ◽  
Author(s):  
Angelica Ginnante ◽  
François Leborne ◽  
Stéphane Caro ◽  
Enrico Simetti ◽  
Giuseppe Casalino
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Parallel Mechanisms ◽  
Serial Manipulators ◽  
Hard Materials ◽  
Serial Robots ◽  
Revolute Joints ◽  
Machining Robot ◽  
Kinematic Models ◽  
Kinematic Performance

Abstract The essential characteristics of machining robots are their stiffness and their accuracy. For machining tasks, serial robots have many advantages such as large workspace to footprint ratio, but they often lack the stiffness required for accurately milling hard materials. One way to increase the stiffness of serial manipulators is to make their joints using closed-loop or parallel mechanisms instead of using classical prismatic and revolute joints. This increases the accuracy of a manipulator without reducing its workspace. This paper introduces an innovative two degrees of freedom closed-loop mechanism and shows how it can be used to build serial robots featuring both high stiffness and large workspace. The design of this mechanism is described through its geometric and kinematic models. Then, the kinematic performance of the mechanism is analyzed, and a serial arrangement of several such mechanisms is proposed to obtain a potential design of a machining robot.

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