The Mechanics of Parallel Mechanisms and Walking Machines

1994 ◽  
Vol 208 (6) ◽  
pp. 367-377 ◽  
Author(s):  
S J Zhang ◽  
D J Sanger ◽  
D Howard
Keyword(s):  
Parallel Mechanism ◽  
Virtual Work ◽  
The Body ◽  
Position Vector ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
End Effector ◽  
Walking Machine ◽  
Walking Machines ◽  
Fixed Base

A parallel mechanism is one whose links and joints form two or more serially connected chains which join the fixed base and the end effector The mechanism of a multi-legged walking machine can be considered as a parallel mechanism whose base is not fixed and whose configuration changes during different phases of its gait. This paper presents methods for analysing the mechanics of parallel mechanisms and walking machines using vector and screw algebra Firstly, displacement analysis is covered; this includes general methods for deriving the position vector of any joint in any leg and for calculating the active joint displacements in any leg. Secondly, velocity analysis is covered which tackles the problem of calculating active joint velocities given the velocity, position and the orientation of the body and the positions of the feet. Thirdly, the static analysis of these classes of mechanisms using the principle of virtual work and screw algebra is given. Expressions are derived for the actuator forces and torques required to balance a given end effector (or body) wrench and, in the case of a walking machine, the ground reactions at the feet. Numerical examples are given to demonstrate the application of these methods.

Relevance and Transferability for Parallel Mechanisms With Reconfigurable Platforms

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Xi Kang ◽  
Jian S. Dai
Keyword(s):  
System Theory ◽  
Parallel Mechanism ◽  
Geometric Model ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Kinematic Coupling ◽  
Reconfigurable Platforms ◽  
Reconfigurable Platform

The parallel mechanism with a reconfigurable platform retains all advantages of parallel mechanisms and provides additional functions by virtue of the reconfigurable platform, leading to kinematic coupling between limbs that restricts development of the mechanism. This paper aims at dealing with kinematic coupling between limbs by investigating the transferability of limb constraints and their degrees of relevance to the platform constraints based on the geometric model of the mechanism. The paper applies screw-system theory to verifying the degree of relevance between limb constraint wrenches and platform constraint wrenches, and reveals the transferability of limb constraints, to obtain the final resultant wrenches and twists of the end effector. The proposed method is extended to parallel mechanisms with planar n-bar reconfigurable platforms, spherical n-bar reconfigurable platforms, and other spatial reconfigurable platforms and lends itself to a way of studying a parallel mechanism with a reconfigurable platform.

A Quasi-Static Model for Planar Compliant Parallel Mechanisms

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Cyril Quennouelle ◽  
Clément Gosselin
Keyword(s):  
Parallel Mechanism ◽  
Applied Load ◽  
Jacobian Matrix ◽  
Static Model ◽  
Parallel Mechanisms ◽  
Compliance Matrix ◽  
End Effector ◽  
Kinematic Constraints ◽  
Compliant Parallel Mechanism ◽  
External Loads

In this paper, the mobility, the kinematic constraints, the pose of the end-effector, and the static constraints that lead to the kinematostatic model of a compliant parallel mechanism are introduced. A formulation is then provided for its instantaneous variation—the quasi-static model. This new model allows the calculation of the variation in the pose as a linear function of the motion of the actuators and the variation in the external loads through two new matrices: the compliant Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism. Finally, a simple application to a planar four-bar mechanism is presented to illustrate the use of this model and the new possibilities that it opens, notably the study of the kinematics for any range of applied load.

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 Collision-free workspace of parallel mechanisms based on an interval analysis approach

Robotica ◽  
2016 ◽  
Vol 35 (8) ◽  
pp. 1747-1760 ◽  
Author(s):  
MohammadHadi FarzanehKaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro
Keyword(s):  
Interval Analysis ◽  
Parallel Mechanism ◽  
Spherical Shape ◽  
Stewart Platform ◽  
Analysis Approach ◽  
Parallel Mechanisms ◽  
Planar Case ◽  
End Effector ◽  
Mechanical Interference

SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

A 3-ṞPR Parallel Mechanism With Singularities That are Self-Motions

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Novona Rakotomanga ◽  
Ilian A. Bonev
Keyword(s):  
Parallel Mechanism ◽  
Control Strategies ◽  
Joint Space ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
Cartesian Space ◽  
Three Degree Of Freedom

The Cartesian workspace of most three-degree-of-freedom parallel mechanisms is divided by Type 2 (also called parallel) singularity surfaces into several regions. Accessing more than one such region requires crossing a Type 2 singularity, which is risky and calls for sophisticated control strategies. Some mechanisms can still cross these Type 2 singularity surfaces through “holes” that represent Type 1 (also called serial) singularities only. However, what is even more desirable is if these Type 2 singularity surfaces were curves instead. Indeed, there exists at least one such parallel mechanism (the agile eye) and all of its singularities are self-motions. This paper presents another parallel mechanism, a planar one, whose singularities are self-motions. The singularities of this novel mechanism are studied in detail. While the Type 2 singularities in the Cartesian space still constitute a surface, they degenerate into lines in the active-joint space, which is the main result of this paper.

The Manta and the Kanuk: Novel 4-DOF Parallel Mechanisms for Industrial Handling

1999 ◽  
Author(s):  
Luc H. Rolland
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Parallel Robot ◽  
Chain Structure ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Low Mass ◽  
Loading And Unloading ◽  
Very High

Abstract Two novel 4-DOF very fast parallel robots were designed. This paper introduces the new parallel mechanism designs which are named the Manta and the Kanuk. In order to reduce manipulator overall costs, the actuator and encoder numbers are minimized to the exact effective degrees-of-freedoms (DOF) which is usually not the case in most parallel robot designs. The robots allow end-effector displacements along the three Cartesian translations and one platform transversal rotation. The two remaining rotations are blocked by the intrinsic mechanical structure including the rotation along the platform normal which is always limited in range. The main advantages are high stiffness through the multiple kinematic chain structure which allow for low mass designs. Moreover, they feature simple mechanical construction. Thus, it shall be possible to achieve very high throughput since high accelerations are feasible. To circumvent the known workspace limitations, the actuators were selected to be prismatic along linear axes. The applications are automated warehouse manipulation, mediatheque manipulation, machine tool tool changers, loading and unloading.

A Study of the Planar Serial-Parallel Mechanism With Various Stiffness for a Biotic Compliant Fish

2013 ◽  
Author(s):  
Cui Zuo ◽  
Jiang Hong-zhou
Keyword(s):  
Simulation Model ◽  
Strouhal Number ◽  
Parallel Mechanism ◽  
Swimming Performance ◽  
Variable Stiffness ◽  
The Body ◽  
Robotic Fish ◽  
Driving Frequency ◽  
Parallel Mechanisms ◽  
Forward Speed

Previous biological experiments show that the fish use their muscles to stiffen their bodies for improving the swimming performance. Inspired by that, we propose a planar model of oscillatory propulsor with variable stiffness using hyper redundant serial-parallel mechanisms to mimic a fish. Our goal in the paper is to identify the swimming characteristics with respect to the body stiffness. Moreover, a simulation model is presented and its results show that the swimming performance is largely dependent on the body stiffness and the driven frequency. Our primary conclusions include: 1) when the driven frequency is closed to the design frequency, the robotic fish with the calculated body stiffness has a super swimming performance. 2) Driven at the design frequency, the forward speed of robotic fish is linearly proportional to the driving frequency and the Strouhal number is consistent with the experiment results 0.25<St<0.35.

Optimal trajectory planning considering optimal torque distribution of redundantly actuated parallel mechanism

2018 ◽  
Vol 232 (23) ◽  
pp. 4410-4419 ◽  
Author(s):  
Sumin Park ◽  
Jongwon Kim ◽  
Giuk Lee
Keyword(s):  
Parallel Mechanism ◽  
Optimization Procedure ◽  
Optimal Operation ◽  
Operation Planning ◽  
Parallel Mechanisms ◽  
Planning Stage ◽  
End Effector ◽  
Torque Distribution ◽  
Redundantly Actuated ◽  
Two Stages

Previous studies on the optimal operation planning of redundantly actuated parallel mechanisms have focused on optimal torque distribution for a predefined trajectory. However, the optimized result obtained for a predefined trajectory cannot guarantee an optimal operation plan, because the torque distribution ability of a redundantly actuated parallel mechanism is highly dependent on the shape of the end-effector trajectory. Therefore, we can expect the redundantly actuated parallel mechanism performance to be enhanced when both the trajectory and torque distribution are optimized during the optimal operation planning stage. We propose a novel redundantly actuated parallel mechanism optimization procedure that can optimize both the end-effector trajectory and torque distribution. The proposed procedure is composed of two stages of optimizers, i.e. upper- and lower-level optimizers that generate the end-effector trajectory and distribute the torques along the generated trajectory, respectively. Composition of these two stages of the optimization procedure allows optimization of both the trajectory and torque distribution, despite the correlation between them. The proposed optimization procedure is simulated using two types of cost functions. All the simulation results show that the proposed procedure facilitates optimization of the end-effector trajectory and the torque distribution concurrently. Also, the cost function value is minimized to a greater extent than in the result with the optimal torque distribution along the initial trajectory.

Kinematic Analysis and Design of Planar Parallel Mechanisms Actuated With Cables

2000 ◽  
Author(s):  
Guillaume Barrette ◽  
Clément M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Analysis And Design ◽  
Spring Mechanism

Abstract In this paper, we present a general and systematic analysis of planar parallel mechanisms actuated with cables. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is denned, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable sub-workspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Guillaume Barrette ◽  
Cle´ment M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Two Dimensional ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Spring Mechanism

In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

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