Compliant Parallel Mechanism Research Articles

Design and performance analysis of a composite flexure hinge based on micro-ultrasonic powder molding

This paper presents a new type of flexure hinge and its fabrication method based on micro-ultrasonic powder molding (micro-UPM). A right-circular notch-type flexure hinge (RFR-RC hinge) comprising an aluminum alloy 7075 (Al 7075) rigid structure and a polypropylene (PP) flexible structure was designed and fabricated. This composite RFR-RC hinge was experimentally studied, and the results helped confirm that the hinge could be considered a complete single structure; the flexible structure had a good forming quality, and the interlocking performance met normal use requirements. The RFR-RC hinge was evaluated in terms of its motion range, stiffness, and stiffness ratio through finite element analysis (FEA) and then compared with a single-material right-circular flexure hinge (RC hinge). The RFR-RC hinge provided a significantly wider operation range with a lower actuation force than the Al 7075-RC hinge and a higher motion pureness and accuracy than the PP-RC hinge. The motion stiffness obtained from the FEA was in agreement with the bending test results, thus validating the FEA results to some extent. From the bending tests, the elastic and total motion ranges of the RFR-RC hinge were found to be 0.068 rad and 0.202 rad, respectively. Finally, the fabrication of a 3-RRR compliant parallel mechanism and four typical applications were taken as examples to demonstrate that the RFR-RC hinge and its fabrication method have a wide range of applications.

Optimization of Desired Multiple Resonant Modes of Compliant Parallel Mechanism Using Specific Frequency Range and Targeted Ratios

In this paper, a dynamic optimization method capable of optimizing the dynamic responses of a compliant parallel mechanism (CPM), in terms of its multiple primary resonant modes, is presented. A novel two-term objective function is formulated based on the specific frequency range and targeted ratios. The first term of the function is used to optimize the first resonant mode of the CPM, within a specific frequency range. The obtained frequency value of the first mode is used in the second term to define the remaining resonant modes to be optimized in terms of targeted ratios. Using the proposed objective function, the resonant modes of a CPM can be customized for a specific purpose, overcoming the limitations of existing methods. A 6-degree-of-freedom (DoF) CPM with decoupled motion is synthesized, monolithically prototyped, and investigated experimentally to demonstrate the effectiveness of the proposed function. The experimental results showed that the objective function is capable of optimizing the six resonant modes within the desired frequency range and the targeted ratios. The highest deviation between the experimental results and the predictions among the six resonant modes is found to be 9.42%, while the highest deviation in the compliances is 10.77%. The ranges of motions are found to be 10.0 mm in the translations, and 10.8° in the rotations.

Design of a Three-Axis Force Sensor Using Decoupled Compliant Parallel Mechanisms

Design of a Three-Axis Force Sensor Using Decoupled Compliant Parallel Mechanisms

Dynamic Modeling and Experimental Verification of an RPR Type Compliant Parallel Mechanism with Low Orders

Efficiency of calculating a dynamic response is an important point of the compliant mechanism for posture adjustment. Dynamic modeling with low orders of a 2R1T compliant parallel mechanism is studied in the paper. The mechanism with two out-of-plane rotational and one lifting degrees of freedom (DoFs) plays an important role in posture adjustment. Based on elastic beam theory, the stiffness matrix and mass matrix of the beam element are established where the moment of inertia is considered. To improve solving efficiency, a dynamic model with low orders of the mechanism is established based on a modified modal synthesis method. Firstly, each branch of the RPR type mechanism is divided into a substructure. Subsequently, a set of hypothetical modes of each substructure is obtained based on the C-B method. Finally, dynamic equation of the whole mechanism is established by the substructure assembly. A dynamic experiment is conducted to verify the dynamic characteristics of the compliant mechanism.

A configuration design approach to the capacitive six-axis force/torque sensor utilizing the compliant parallel mechanism

The configuration of capacitive six-axis force/torque (F/T) sensors significantly impacts their performance, and there are few studies on the configuration design method of the sensor. By analyzing the signal conversion model of the sensor, this paper proposes that the key to obtaining a reasonable configuration is that the configuration can easily achieve sensitivity isotropy. To achieve sensitivity isotropy, the six-degree-of-freedom sensitive part must be available. The compliant parallel mechanism is easier to meet this requirement. Based on the position and orientation characteristic (POC) set theory, the flexure building blocks applicable to compliant sensitive part configurations are analyzed, and we investigate a methodology for synthesizing compliant parallel sensor configurations that satisfy sensitivity isotropy. The results show that the precision is 0.66%FS in the physical prototype experiment, the fabricated sensor has good performance. The proposed configuration design methodology proposed can effectively guide the design of the capacitive six-axis F/T sensor.

A Synthesis Approach of XYZ Compliant Parallel Mechanisms Toward Motion Decoupling With Isotropic Property and Simplified Manufacturing

Abstract Decoupled compliant parallel mechanisms with isotropic legs possess many excellent performances, including ease of actuation, control, manufacture and mathematical analysis, as well as effective error compensation. Despite the advent of numerous isotropic compliant parallel mechanisms, their synthesis process predominantly relies on the empirical knowledge of engineers, with an absence of dedicated synthesis methodologies. This paper proposes the constraint algebra method, a novel synthesis method capable of autonomously exploring feasible constraint space for the synthesis. This method involves algebraic formulation of the constraints for the compliant modules, followed by solving constraint equations to find the feasible constraints and orientations, thereby facilitating the synthesis with intended performance characteristics. The multiplicity of solutions to the constraint equations enables the generation of diverse designs, including innovative configurations that are challenging to obtain via other methods and experience. Furthermore, by the consideration of machinability in several steps of synthesis, the optimal configuration can be selected for simplified manufacture. A design case has been monolithically prototyped and experimentally tested. The proposed methodology holds promise for potential extension to the synthesis of other types of compliant mechanisms.

A spatial 3-DOF piezoelectric robot and its speed-up trajectory based on improved stick-slip principle

Piezoelectric robots have been proven to be suitable for high-precision, cross-scale micro-nano manipulation due to their nanometre resolution and high flexibility. To make up for the limited stroke of micro-nano positioning platforms, a spatial three-degrees-of-freedom (3-DOF) piezoelectric robot is proposed in this study to enable three-dimensional micro-nano manipulation of objects. The robot utilizes the deformation of the piezoelectric stack as the source of displacement. It is comprised of a parallel compliant mechanism and a guided compliant mechanism in series, resulting in a compact robot body. The robot is capable of linear displacement in x-, y- and z-axes. The stiffness of the guided compliant mechanism is calculated using theoretical modeling and compared with the finite element simulation results, with a deviation of less than 5.6% verifying the accuracy of the model. The robot operates using two motion principles: the direct drive principle, which has a resolution of 16, 15, and 11 nm in x-, y- and z-axes, and a motion space of 13×11×7 μm3; and the improved stick-slip principle, which has a theoretical infinite stroke and a maximum speed of 4.2 and 3.9 mm/s in x- and y-axes. The speed of the improved stick-slip principle is 42% higher than that of the traditional stick-slip principle in x- and y-axes. The robot has a spatial 3-DOF, nanometre resolution, millimeter speed, and can carry more than 500 g.

Dynamic modeling and optimization of mechanical drift for compliant parallel micromanipulation driven by V-shape linear ultrasonic motors

Designing micro-mechanisms that satisfy large strokes, high precision, and multiple degrees of freedom has consistently been a research focus and challenge in the field of micromanipulation systems. Linear ultrasonic motors (LUMs), with advantages such as millimeter-level travel, nanometer-level motion resolution, and power-off self-locking, significantly contribute to the advancement in the mechanism design of micromanipulation systems. However, the challenge of mechanical drift lacks a comprehensive theoretical analysis to explain its cause and limits its application. This paper presents a mechanical drift modeling method for a compliant parallel micromanipulation (CPM) driven by a LUM. The model primarily focuses on the creep characteristics of the flexure clamp element in the LUM. Based on the stiffness matrix analysis method of the compliant parallel mechanism kinematics, the mechanical drift dynamics model of the CPM is established. The influence of the main structural parameters on the CPM mechanical drift is investigated. The research indicates that the creep of flexure clamps in the CPM is the main factor leading to the mechanical drift. Optimization of mechanical drift is achieved by choosing flexure clamps with higher tangential stiffness for LUM and flexure hinge joints with greater flexibility for CPM. Finally, experimental studies reveal that under equivalent conditions, the mechanical drift of the optimized CPM was significantly reduced than before, proving the rationality of the theoretical model and optimization method.

Development of a novel monolithic compliant Lorentz-force-driven XY nanopositioning system

A novel monolithic compliant Lorentz-force-driven XY nanopositioning system (MCLNS) is designed, analyzed, and experimentally assessed with the aim of high-resolution positioning across a large workspace. A double-symmetric Lorentz-force actuator (DSLA) with the benefits of zero friction, high thrust, and large stroke is proposed to generate the actuation force. Correspondingly, a monolithic four-prismatic parallel compliant mechanism (4P-PCM) is exploited to transmit the actuation motion to the central platform and minimize the parasitic motion. The unique integration of four DSLAs and one 4P-PCM make the proposed MCLNS possess compact structure and stable performance. The characterization of the MCLNS is formulated by a specially established analytical model and validated by finite-element analysis simulation and experimental tests. Experimental studies show that the workspace of the MCLNS prototype is large than 0.87 × 0.87 mm2 and the positioning resolution of the MCLNS prototype is better than 9 nm. By means of a nonlinear forward proportional integral derivative control strategy, the maximum contouring error of the MCLNS is maintained within 2.7% while tracking a 1257 μm s−1 circular trajectory.

Enabling the transfer matrix method to model serial–parallel compliant mechanisms including curved flexure beams

AbstractCompliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces, low stress levels, and flexible design parameters, which have attracted considerable attention in precision engineering, metamaterials, robotics, and so forth. However, serial–parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design. Here, the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial–parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods. Consequently, serial–parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step‐by‐step procedure. Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach. In conclusion, the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial–parallel compliant mechanisms and beam structures, including curved flexure hinges and irregular‐shaped rigid bodies.

Modeling and control for a long-stroke 4-PPR compliant parallel mechanism

Modeling and control for a long-stroke 4-PPR compliant parallel mechanism

Synthesis of Compliant Parallel Mechanisms Using an Improved Beam-Based Method with the Optimization of Multiple Resonant Modes

This paper proposes an improved beam-based method to synthesize a compliant parallel mechanism (CPM) with multiple degrees of freedom (DoFs). The proposed method utilizes a structural optimization technique to synthesize a three-legged CPM with a single-beam structure constructed by two perpendicular segments in each leg to achieve the desired DoFs and fully decoupled motion. In addition, an objective function is proposed to optimize the primary resonant frequencies in actuating directions to targeted values to achieve the desired dynamic behaviors. A 4-DoF CPM, with one translation and three rotations, is synthesized using the improved beam-based method and all of the primary resonant frequencies are optimized to the targeted values. The 4-DoF CPM prototype is fabricated monolithically and evaluated experimentally in terms of its mechanical characteristics, workspace, and resonant modes. The obtained results show that the experimental stiffness and dynamic properties agree with the predictions. In particular, the prototype has good motion decoupling capability, as reflected by the high stiffness ratios of more than 500 between the non-actuating and actuating directions; the large workspaces of up to 4.0 mm and 7.2° for the translation and rotations, respectively; and the resonant frequencies being close to the targeted ones. In addition, the highest deviations between the predicted and experimental results are 9.49% and 9.13% for the stiffness and dynamic behaviors, respectively, demonstrating the correctness and effectiveness of the proposed method.

Modeling and control system design of 6-DOF bionic parallel mechanism with compliant modules

Quadrupeds are capable of dynamic movements such as fast running and long-distance jumping due to their flexible and elastic torso structures. In this paper, a compliant parallel mechanism is proposed as a bionic torso to simulate the diversified behaviors and agile locomotion of the tetrapod torso. The spring module is incorporated into the limb of the parallel mechanism to absorb external shocks, cushion, and dampen vibrations, thus improving the compliance performance of the bionic torso. For the compliant parallel mechanism, its kinematics and kinetics are analyzed, and the overall electromechanical system and control framework are devised. The multidimensional damping dynamic characteristics of the proposed mechanism are qualitatively analyzed by simplifying the limb into a spring–mass damping system. The parallel mechanism with compliant spring modules absorbs external forces to different degrees with different stiffness coefficients to avoid damage to the structure by external impacts. The parallel mechanism with different initial positions exhibits the inherent variable stiffness characteristics of the mechanism. The parallel mechanism simulates the diverse behavior of the animal torso, with independent and synthesized locomotor behavior of the six underlying motion patterns. Simulations and experiments demonstrated that the compliant parallel mechanism is effective in vibration damping and cushioning, with a rapid response and small steady-state error. The motion of the compliant parallel mechanism in one direction and the motion of the integrated multi-degree of freedom (DOF) are confirmed and exhibited in the behavioral experiment.

Modeling and Analysis of a Novel 3R Parallel Compliant Mechanism

This paper presents and investigates a new three-rotation (3R) parallel compliant mechanism that uses compliant rods to achieve three rotations. The mechanism is designed for use in pointing devices or as a spatial parallel manipulator. The mobility analysis is based on the Cosserat rod model and Lagrangian dynamics equations. The dynamics equations are then effectively solved using the back-propagation neural network and chaos-enhanced accelerated particle swarm optimization. After studying the mobility of the moving platform, a simplified model is proposed and used for kinematic analysis. The analysis of motion includes discussions on forward kinematics, inverse kinematics, singularities, and the workspace. Furthermore, experiments with a prototype are conducted to verify the accuracy and stability of the mobility analysis and the simplified model.

An Inverse Kinematic Model for the 3-PRS Compliant Parallel Mechanism With Forward Causative Force

An Inverse Kinematic Model for the 3-PRS Compliant Parallel Mechanism With Forward Causative Force

The compliant version of the 3-RRR spherical parallel mechanism known as “Agile-Eye”: Kinetostatic analysis and parasitic displacement evaluation

The compliant version of the 3-RRR (R - revolute joint) spherical parallel mechanism known as “Agile-Eye” is presented. The kinetostatic analysis of this Compliant Spherical Parallel Mechanism (CSPM) is conducted using the Compliance Matrix Method (CMM) evaluating two different types of Rotational Compliant Joints (RCJs) and with three inputs. These independent inputs could be forces or displacements. Expressions that relate the input forces/displacements with the displacement of the moving platform are obtained from the kinetostatic analysis. These expressions are used to obtain the required inputs to perform a rotational trajectory of the moving platform; parasitic displacements are computed during this process. Analytical results are validated through Finite Element Analysis (FEA). Additionally, the CSPM geometric parameters-parasitic displacements relation is characterized. Those parameters resulting with lower parasitic displacements are determined. Finally, expressions from the kinetostatic analysis are corroborated experimentally using input displacements in a manufactured prototype with parameters selected to have reduced parasitic displacements. Results from the FEA-simulations and experimental tests demonstrated that the expressions obtained from the kinetostatic analysis can accurately describe the force–displacement relations of the proposed CSPM.

Kinematic modeling of a spatial three degrees-of-freedom compliant micro-motion parallel mechanism considering input coupling effect and bilateral restrained torsion

PurposeThis paper aims to improve the kinematic modeling accuracy of a spatial three-degrees-of-freedom compliant micro-motion parallel mechanism by proposing a modified modeling method based on the structural matrix method (SMM).Design/methodology/approachThis paper analyzes the problem that the torsional compliance equation of the circular notched hinge is no longer applicable because it is subject to bilateral restrained torsion. The torsional compliance equation is modified by introducing the relative length coefficient. The input coupling effect, which is often neglected, is considered in kinematic modeling. The symbolic expression of the input coupling matrix is obtained. Theory, simulation and experimentation are presented to show the validity of the proposed kinematic model.FindingsThe results show that the proposed kinematics model can improve the modeling accuracy by comparing the theoretical, finite element method (FEM) and experimental method.Originality/valueThis work provides a feasible scheme for CMPM kinematics modeling. It can be better applied to the optimization design based on the kinematic model in the future.

Design and Performance of a Spatial 6-RRRR Compliant Parallel Nanopositioning Stage

Piezoelectric actuators (PEAs) and compliant parallel mechanisms (CPMs) are advantageous for designing nanopositioning stages (NPSs) with multiple degrees of freedom (multi-DOFs). This paper proposes a new NPS that uses PEAs and CPMs with multiple spatial DOFs. First, the design of the mechanism is introduced. Six parallel kinematics revolute-revolute-revolute-revolute (RRRR) branched chains were used to create a 6-RRRR CPM for superior mechanical performance. Three in-plane and three out-of-plane chains were combined using a two-in-one structure to ensure fabrication feasibility. A two-in-one 6-RRRR CPM was employed to build the proposed NPS. Second, the mechanical performance was analyzed. High-efficiency finite-element modeling approaches were derived using the compliance-based matrix method (CMM) and a pseudo-rigid body model (PRBM). The model included both 6-RRRR CPM and NPS. The simulation results validated the static and dynamic performance, and the experimental results verified the kinematics. Based on the newly designed mechanism and verified mechanical performance, the proposed 6-RRRR NPS contributes to the development of spatial multi-DOF NPSs using PEAs and CPMs.

Topology optimization of a spatial compliant parallel mechanism based on constant motion transmission characteristic matrix

This paper presents a new method of constructing spatial fully compliant parallel mechanisms. The constant motion transmission characteristic matrix of a spatial 3-degree-of-freedom (DOF) compliant mechanism is used as the constraint function of topology optimization to control the relationship between input and output. A multiobjective topology optimization formula with determined weighting factors is proposed to solve the common input–output coupling problem. This strategy maps the motion characteristics of the original mechanism to the compliant mechanism rather than considering how to use the flexible hinge to replace the rigid hinge. We choose a 3-CPR parallel mechanism with constant motion transmission characteristics as an example to construct a topology optimized compliant mechanism. A series of simulations and experiments proved that the compliant mechanism has higher motion accuracy and a linear mapping relationship between inputs and outputs, and it is isomorphic with the original 3-CPR parallel mechanism.

A constraint-flow based method of synthesizing XYθ compliant parallel mechanisms with decoupled motion and actuation characteristics

It is an open challenge to synthesize XYθ compliant parallel mechanisms (CPMs) with decoupled motion and actuation characteristics for increasing applications from semiconductor manufacture to bio-nanotechnology. The key issue in the synthesis is to obtain the permitted constraints of the constituent compliant modules. In this paper, a constraint-flow based method is proposed to address this need, and up to 6859 constraint combinations are derived for the compliant modules, leading to a great number of possible synthesis schemes. Two case studies of schemes are presented to demonstrate the proposed synthesis method. One of the designs is analytically modelled, with less than 6.45% difference compared with the FEA results. A prototype of the design is also fabricated and experimentally tested. The analytical, FEA and/or experimental results show that the couplings are less than 3.9%, the translation resolution is 5 nm, and the rotation resolution is 50 nrad. The introduced constraint flow concept is not limited to the application of synthesizing decoupled XYθ CPMs, but also is an alternative and effective method in synthesizing other types of CPMs.