Parasitic Motion Research Articles

Comparison of 3-[PP]S-Y Spatial Parallel Manipulators based on link tolerances and parasitic motions

This paper strives to compare between two 3-Degree of Freedom (DoF) Spatial Parallel Manipulators (SPMs) belonging to the 3-[PP]S-Y family viz., 3-RRS and 3-RPS. The planes of the manipulators belong to this family are arranged in a Y-pattern such that they intersect at 120° in a common line. Both of these manipulators have a common motion of 1T2R (T: Translation, R: Rotation) type, and their comparison in this work is carried out by considering the effects of link tolerance and parasitic motions, for the same task space and End-Effector (EE) positions. Their respective position kinematic analysis is discussed initially. The comparison is then carried out by considering two different cases based on the sizes of the moving platform relative to the base platform. The errors are quantified and all the comparative results are represented with the aid of plots. The conclusions are summarized at the end that allow to know the better of the two manipulators for the given effects.

Voice coil motor-driven multi-DOF compliant parallel micropositioning stage based on a large range beam-based spherical hinge and fully symmetrical layout

With the recent rapid developments in the field of precision engineering, demand for the large range multi-degrees-of-freedom (DOF) micropositioning stage has increased significantly. In this paper, to solve the problems of small motion range, local stress concentration, and low motion accuracy caused by the parasitic motion of the traditional flexure hinge in the multi-DOF micropositioning stage, we first propose a type of large-range beam-based flexure spherical hinge (BFSH). Subsequently, based on the proposed BFSH, a large range 3-DOF θxθyz spatial micropositioning stage driven by the voice coil motor is designed employing parallel branch chains and a fully symmetrical layout. This arrangement realizes theoretical motion decoupling in structural design. Furthermore, we use the geometric method to derive kinematic equations of the moving platform, which are used as the decoupling matrix of the control loop. Based on the compliance matrix method and Lagrange’s method, the compliance matrix model of the BFSH, the 3-DOF micropositioning stage, and the stage dynamic model are determined respectively. Additionally, finite element analysis and experimental tests are conducted to verify the accuracy of the analytical model and assess the static and dynamic performance of the designed 3-DOF stage. Moreover, a fractional order phase advanced proportional integral controller is designed for closed-loop control to track the sinusoidal trajectory and spherical trajectory. The results reveal that the stage can achieve the desired large workspace of ± 21.5 mrad × ± 20.3 mrad × ± 3.23 mm, as well as excellent decoupling and trajectory tracking performance.

Workspace optimization of 1T2R parallel manipulators with a dimensionally homogeneous constraint-embedded Jacobian

This paper presents the workspace optimization of one-translational two-rotational (1T2R) parallel manipulators using a dimensionally homogeneous constraint-embedded Jacobian. The mixed degrees of freedom of 1T2R parallel manipulators, which cause dimensional inconsistency, make it difficult to optimize their architectural parameters. To solve this problem, a point-based approach with a shifting property, selection matrix, and constraint-embedded inverse Jacobian is proposed. A simplified formulation is provided, eliminating the complex partial differentiation required in previous approaches. The dimensional homogeneity of the proposed method was analytically proven, and its validity was confirmed by comparing it with the conventional point-based method using a 3-PRS manipulator. Furthermore, the approach was applied to an asymmetric 2-RRS/RRRU manipulator with no parasitic motion. This mechanism has a T-shape combination of limbs with different kinematic parameters, making it challenging to derive a dimensionally homogeneous Jacobian using the conventional method. Finally, optimization was performed, and the results show that the proposed method is more efficient than the conventional approach. The efficiency and simplicity of the proposed method were verified using two distinct parallel manipulators.

Adjustable, radii-controlled embedded lamina (RadiCEL) hinges for folding of thick origami-adapted systems

This work presents a method for creating hinge-like motion for origami-adapted mechanisms using internal membranes attached between rigid panels. The goal is to remove adhesive requirements, preserve panel volume for use as hard stops, and reduce parasitic motion experienced by other membrane joint types, while keeping the stress in the membrane below the stress limits. Two configurations are presented. The first is the general case called the radii-controlled embedded lamina (RadiCEL) hinge. The second is a special case and is referred to as the Radii-Controlled Regionally Sandwiched Compliant Sheets (RC-ReCS). These two configurations are described for a planar, single-folding mechanism with a description of ways in which the adjustability can be utilized to benefit various design requirements. A comparison between methods is presented, focusing on the axial parasitic motion of each configuration. Each configuration is applied to a degree-4 origami vertex, with a discussion of the benefits of each and a multi-vertex pattern is also presented. Finally, the RadiCEL hinge is presented as the hinge used in a foldable metasurface antenna.

Parasitic Motions of 3-PRS Parallel Mechanisms with Two Different Branch Chain Arrangements

The kinematics of 3-PRS parallel mechanisms (PMs), an important category of 2R1T PMs, is very important for the motion control and error compensation of PMs. In order to produce a spindle head that could meet the requirements of various machining accuracy levels, a definite kinematics analysis of the PMs par should be taken with caution firstly. Here, the mathematical models of two 3-PRS PMs with different branch chain arrangements were established using the Euler angle. The kinematic equations of two 3-PRS PMs were obtained by establishing the closed-vector loop equation according to structural conditions. Parasitic motions that would cause a great effect were obtained, and their variations with structural and kinematic parameters were also obtained through MATLAB. Since the relationship between parasitic motions, and the given structural and kinematic parameters, is inextricable, an analysis is performed for the purpose of reducing or eliminating parasitic motion to ensure the accuracy of end-effector movement. The caused effect of parasitic motion can be improved with scale optimization and precision compensation. Lastly, two improved 3-PRS PMs without the parasitic motion of different branch chain arrangements used as the spindle head were obtained. Parasitic motion was related to the mechanism configuration and could be avoided in the configuration design stage with the comprehensive optimization of the structural and kinematic parameters, which provides a reference to obtain a sufficient workspace and improve the precision of traditional five-axis CNC machine tools.

Three 2-DOF 1T1R and One 3-DOF 2T1R Full-Hinged Novel Parallel Mechanisms With Zero Coupling Degree and Motion Decoupling: Design and Analysis

AbstractThis paper presents the design and analysis of a family of full-hinged partially-decoupled novel parallel mechanisms (PMs) featuring one/two translation(s) and one rotation (1T1R/2T1R). First, three 2DOF 1T1R and one 3DOF 2T1R novel spatial PMs are proposed, according to topology design theory of PM based on position and orientation characteristic (POC) equations. The 3DOF 2T1R PM is illustrated to show its topological characteristics, such as POC set, degrees-of-freedom (DOF), and coupling degree (k), which show that the PM does not produce parasitic motion, with the coupling degree k being equal to zero. Second, the kinematic and dynamic performances of the 3DOF 2T1R PM are analyzed, including symbolic forward position solutions based on its topological characteristics, the workspace based on both the forward and inverse position solutions, respectively, the singular configurations based on the inverse position solutions, and the dynamic analysis built by means of the virtual work principle based on the single-open-chain units. Finally, the potential application of the proposed 3DOF 2T1R PM, namely, lifting and transferring lightweight workpieces between two perpendicular conveyor belts on the floor, is introduced.

A parasitic-inertia piezoelectric actuator with isosceles trapezoidal flexible mechanism base on parasitic motion exploration and asymmetrical installation

Parasitic-inertia piezoelectric actuators have been widely studied for their ability to achieve both high positioning accuracy and large working strokes. However, backward motion results in parasitic-inertia piezoelectric actuators with the disadvantages of low efficiency and abrasion of driving foot. In this study, a parasitic-inertia piezoelectric actuator with an isosceles trapezoidal flexible mechanism is diegned and optimized to reduce backward motion considering the influence of parasitic motion proportion. It applies the asymmetrical installation of the piezoelectric stack to increase parasitic motion hence the reducing of backward motion. This study discusses the structure and working process of piezoelectric actuators and optimizes the design of flexible mechanism structure parameters with matrix displacement method and finite element method. A prototype of an parasitic-inertia piezoelectric actuator was manufactured, and a series of experiments were conducted. From the experiment, the piezoelectric actuator obtained a minimum backward motion percentage α = 18.36% and forward motion time percentage β = 95.9% at the frequency f = 1 Hz and the voltage U = 80 V. At U = 120 V, f = 500 Hz, the maximum motion speed of the actuator is 916 μm s−1; At U = 20 V and f = 1 Hz, the minimum positioning resolution of the actuator is 0.69 μm. At U = 120 V, f = 1 Hz, the maximum vertical load force is 1600 g, and the maximum parallel load force is 50 g. It has shown that the proposed isosceles trapezoidal flexible mechanism is feasible and can significantly reduce backward motion at the appropriate voltage. The mentioned characteristics of isosceles trapezoidal flexible mechanism can significantly alleviate the abrasion of driving foot, improve working efficiency. Also, it is vital for the miniaturization and practical application of parasitic-inertia piezoelectric actuators.

Characteristics of Statically Indeterminate Symmetric Flexure Structures

Statically indeterminate symmetric (SIS) flexure structures are symmetric structures with “clamped-clamped” boundary conditions. The static indeterminacy and topological symmetry significantly attenuate the parasitic motions associated with statically determinate flexure structures. Hence, SIS flexure structures feature decoupled linear and angular motions, improved motion accuracy, high stiffness, and high stability. Although SIS flexure structures have been more frequently utilized as prismatic joints, they can also be utilized as revolute joints. This study systematically investigates the characteristics of SIS flexure structures. Based on the unified compliance models of a single flexure hinge, analytical compliance models of two fundamental types of SIS flexure structures are established. In 1-degree-of-freedom or planar applications, multiple SIS-based structures can also be integrated into various configurations to transmit linear or angular motions. Corresponding stiffness models are also established. The characteristics and possible applications of the SIS flexure structures are computationally investigated through case studies. Ultimately, several SIS prototypes are manufactured, and the modeling accuracy of the established stiffness models is experimentally verified.

On Constraints and Parasitic Motions of a Tripod Parallel Continuum Manipulator

A parallel continuum manipulator (PCM) is a mechanism of closed-loop morphology with flexible elements such that their deformation contributes to its mobility. Flexible hexapods are six-degrees-of-freedom (DoF) fully parallel continuum mechanisms already presented in the literature. Devices of reduced mobility, i.e., lower mobility than six DoF, have not been studied so far. An essential characteristic of lower mobility mechanisms is that reduced mobility is due to kinematic constraints generated by mechanical arrangements and passive joints. In rigid-link parallel manipulators, those constraints are expressed as a set of equations relating to the parameters representing the end effector’s pose. As a consequence, independent output pose variables are controllable with the position equations, while dependent output variables undergo parasitic motions. In this paper, the performance of a tripod-type parallel continuum manipulator, 3PF̲S, is compared with the operation of its rigid counterpart 3P̲RS. We will show that in PCMs there are no such geometric constraints expressible with algebraic equations, but it is difficult to perform some types of motion in the end effector with the input torques. Another goal of this paper is to evaluate such limitation of motion in a tripod-like PCM and compare it with the constraints of the rigid 3P̲RS. Finally, the paper shows that there are strong similarities in the reduced mobility of both mechanisms.

A novel flexure-based Delta micromanipulator with low parasitic motions

A novel flexure-based Delta micromanipulator with low parasitic motions

Rigid-body inverse dynamics of a spatial redundantly actuated parallel mechanism constrained by two point contact higher kinematic pairs

This paper presents a comparative study of the rigid-body inverse dynamics of a spatial redundantly actuated parallel mechanism constrained by two point contact higher kinematic pairs (HKPs). Firstly, its constrained motions are analysed comprehensively, then four different models are formulated by the generalized momentum approach and the Lagrange-D'Alembert formulation to explore its inverse dynamics. In each method, the first model is built by employing the method directly to the mechanism. In the second model, the dynamic model of its non-redundantly actuated counterpart free of HKPs is built by this approach first, then the constraints from HKPs are modelled, to finally reach the model of the redundantly actuated parallel mechanism (RAPM) where that of its counterpart is utilised as the core. The four models give rise to equivalent numerical results, and the second model in both methods of the RAPM can alleviate the strong coupling between the parasitic motion variables and degrees of freedom (DOFs), boosting the computational speed as fast as that of its non-redundantly actuated counterpart without simplification or loss of accuracy. The comparisons between the mechanism and its counterpart validate that the HKP constraints greatly increase the computational complexity, and the torques required by the parasitic motions of the end effector are significantly smaller than those by the corresponding DOFs.

Topology optimization design of compliant amplification mechanisms with low parasitic displacement

Compliant amplification mechanisms amplify input displacement in the desired output direction. However, owing to structural design, parasitic motion can easily be produced in an unexpected direction. The parasitic motion has a negative effect on the motion accuracy of the mechanism. To solve this problem, a topology optimization method for compliant amplification mechanisms with low parasitic displacement was proposed. Based on the variable density topology optimization method, the topology optimization model of the compliant amplification mechanism was established with the goal of increasing the output displacement and reducing the parasitic displacement. Volume ratio was set as constraint condition. The optimization criterion method were used to solve the problem and topology optimized amplification mechanisms (TOAMs) were obtained. Simultaneously, the configuration characteristics and displacement amplification ratios of the mechanism under different virtual spring stiffnesses were compared. To verify the validity of the method, the performance of the TOAM and the typical amplification mechanism (TAM) were compared using finite element simulation. The displacement amplification ratio is 5.95 and 3.17, and the relative parasitic displacement is 0.6% and 10.27%, respectively. Finally, the performance of the TOAM and the TAM was verified by experiments. The displacement amplification ratio is 5.72 and 3.06, and the relative parasitic displacement is 0.95% and 10.64%, respectively. Simulation and experimental results show that the TOAM has a larger displacement amplification ratio and a lower parasitic displacement, which verifies the validity of this method.

Optimization design of two-stage amplification micro-drive system without additional motion based on particle swarm optimization algorithm

With the increasing requirements of precision mechanical systems in electronic packaging, ultra-precision machining, biomedicine and other high-tech fields, it is necessary to study a precision two-stage amplification micro-drive system that can safely provide high precision and a large amplification ratio. In view of the disadvantages of the current two-stage amplification and micro-drive system, such as poor security, low motion accuracy and limited amplification ratio, an optimization design of a precise symmetrical two-stage amplification micro-drive system was completed in this study, and its related performance was studied. Based on the guiding principle of the flexure hinge, a two-stage amplification micro-drive mechanism with no parasitic motion or non-motion direction force was designed. In addition, the structure optimization design of the mechanism was completed using the particle swarm optimization algorithm, which increased the amplification ratio of the mechanism from 5 to 18 times. A precise symmetrical two-stage amplification system was designed using a piezoelectric ceramic actuator and two-stage amplification micro-drive mechanism as the micro-driver and actuator, respectively. The driving, strength, and motion performances of the system were subsequently studied. The results showed that the driving linearity of the system was high, the strength satisfied the design requirements, the motion amplification ratio was high and the motion accuracy was high (relative error was 5.31%). The research in this study can promote the optimization of micro-drive systems.

A new symmetrical Z-shaped compliant linear actuator based on parasitic motion principle

To meet the demand of designing piezoelectric actuators with long working stroke and high resolution, a new parasitic motion principle (PMP) linear actuator based on the symmetrical Z-shaped compliant mechanism was proposed in this paper. The mechanism design and the operation principle of the proposed linear actuator were elaborated. The theoretical model of the symmetrical Z shaped compliant mechanism deformation was established, and was verified by the simulation analysis. Experimental studies were conducted on a manufactured prototype to investigate the performances of the proposed linear actuator. The results indicate that a linear actuator with bi-directional motion can be achieved, which has a resolution of 106 nm in the forward direction and 84 nm in the reverse direction. Under the locking force of 0.8 N, the maximum speed of 270 µm s−1 was reached, when the amplitude and the frequency of the driving voltage were set to 60 V and 650 Hz. It is also noted that the proposed linear actuator can work with a loading capacity of 25 g. This study has provided an alternative way for the development of a PMP linear actuator with bi-directional motion.

Hierachical micro/nano structures fabrication by a novel tri-axial piezoelectric servo system

In this study, a novel tri-axial piezoelectric servo system is developed for micro/nano manufacturing considering the stroke, motion resolution, crosstalk, working bandwidth, compact structure, and position and pose modulation capability of cutting tool. A compliant mechanism which consists four compliant chains is designed based on trapezoidal leaf spring, X-type flexure hinge and right circular flexure hinge. The structure dimensional parameters are determined by finite element analysis (FEA) optimization method. Analytical modeling for compliance and dynamics are established and verified by FEA. Besides, the prototype of the developed tri-axial piezoelectric servo system was manufactured and experimentally tested. Testing results show that the high stroke, low parasitic motion, high motion resolution as well as the dynamic response can be obtained in terms of the compact structure. Moreover, the tracking control is conducted to demonstrate the controllability of the tri-axial piezoelectric servo system. Finally, the stability and feasibility of the developed system is verified by typical micro/nano structures manufacturing.

Synthesis of Multi-position 3-PRS Manipulator Based on Spherical Constraints by Eliminating the Parasitic Motion

Synthesis of Multi-position 3-PRS Manipulator Based on Spherical Constraints by Eliminating the Parasitic Motion

Development of an Optimized Three-Axis Fast Tool Servo for Ultraprecision Cutting

A three-axis fast tool servo (FTS) with a symmetric structure design to reduce the parasitic motion for realizing high tracking accuracy while maintaining high performances in stiffness and open-loop bandwidth is developed for ultraprecision diamond cutting. Modeling, analysis, and optimization of performances by the finite-element method in six degree-of-freedom are conducted for designing the mechanism. Experiments are carried out to test the performances of the three-axis FTS, which show low parasitic motion, high tracking accuracy, and high dynamic response. With the low tracking error of close-loop control for each axis, complicated trajectory tracking in 3-D space is realized with a tracking error as small as 5 nm. Finally, complicated and irregular microstructures are fabricated by the three-axis FTS to demonstrate the practicability of the FTS.

Low-Coupling Hybrid Parallel-Serial-Kinematic Nanopositioner with Nonorthogonal Flexure: Nonlinear Design and Control

This article focuses on the design and high-precision control of a new dual-stage, three-axis hybrid parallel-serial-kinematic nanopositioner developed specifically for feature-tracking applications with arbitrary scanning directions. Dual-actuation is achieved by integrating a three-axis shear piezoelectric actuator into the large-range planar stage. A novel nonorthogonal compliant motion-amplifying mechanism which reorients the lateral sample-platform displacement to align with the principal directions of the input piezoactuators is used to minimize parasitic (coupling) motion. A nonlinear rigid-link model and finite element analysis (FEA) are used to optimize over the orientation parameter during the design process. A prototype stage is manufactured and tested, and the lateral and vertical travel ranges are approximately 18 × 21 and 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m, respectively, with secondary lateral actuation in the range of 1 × 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m. Coupling in the long-range stage is below -31 dB for both axes, an estimated 51 to 86% reduction compared to a traditional perpendicular-mechanism design. The measured dominant resonances for the lateral directions of the long-range stage are approximately 1.4 kHz, while short-range positioner resonances are approximately 11 and 40 kHz for the lateral and vertical directions, respectively. The design of a new feedforward-feedback controller is described, and the controller is implemented with field-programmable gate array (FPGA) hardware, where individual actuator contributions are intuitively determined by shaping the frequency response of their relative and summed displacements. An inverse hysteresis operator is used to linearize the plant behavior for effective motion control. Experimental tracking and atomic force microscopy (AFM) imaging results are presented to demonstrate the performance of the new mechanical and control system designs.

A Novel Method for Type Synthesis of Parallel Mechanism Without Parasitic Motion Based on 2R1T Parallel Mechanism with Rotational Bifurcation

The parasitic motion has been widely recognized as the major drawback of the parallel mechanism. Therefore a class of 2R1T PMs (parallel mechanism) without parasitic motion has been synthesized. However, these PMs can only rotate around two axes in sequential order. It decreases the performance of the balancing adjustment of the end-effector. In this paper, a family of 2R1T PMs without parasitic motion was reconstructed by using a novel method based on the remarkable properties of rotational bifurcation mechanisms, which can rotate in sequential order. Furthermore, some PMs rotating around two continuous axes in an arbitrary order are established by adding single joints. Taking the practicability of these structures into consideration, the workspace of 3-PRPS PM was analyzed as an example. Moreover, this study explores the practical application of the PMs without parasitic motion in developing balance mechanisms in rough-terrain fire-fighting robots. During the climbing process, the tank is adjusted to be parallel to the horizontal plane in real-time. It is proved that this kind of structure realizes continuous rotation around two rotation axes on the premise of no parasitic motion.

A novel large stepping-stroke actuator based on the bridge-type mechanism with asymmetric stiffness

This paper presents the design, analysis, and experiments of a novel stick–slip actuator with large working stroke and high resolution based on parasitic motion. To meet the requirement on large stepping-stroke in the fields of nanofabrication and nano-characterization, the bridge-type mechanism with asymmetric stiffness which changes the distribution of piezoelectric actuator elongation at two input points is proposed. A chain-based compliance matrix model is established for the static performance characterization and parameter optimization of the dual-input closed-loop compliant mechanism, and the performance is further studied by finite element method. The prototype of the proposed actuator is manufactured and experimental tests are conducted to investigate its characteristics. The results indicate that the maximum motion speed is 23.53 mm/s with the driving frequency of 350 Hz. The stepping-stroke is 102 μm, and the resolution is measured to be 12 nm. It is confirmed that the proposed actuator is feasible to enlarge the stepping-stroke and work stably.