Effect of novel continuous friction model on nonlinear dynamics of the mechanisms with clearance joint

A general methodology for the dynamic modelling and analysis of planar multi-body systems with a continuous friction model in joint clearance is presented. Joint clearance is the critical factor that influences the dynamic response and the performance of mechanisms for high-speed application. In light of recent developments in the joint clearance studies, the number of contact force models has been introduced with ignoring friction continuity. The selection of an appropriate continuous friction model is still challenging and essential, which requires further development. Therefore, a perfect continuous friction model, including the Stribeck effect, static, dynamic and viscous friction terms, is proposed and validated. Investigating the dynamic modelling and analysis of double rocker four-bar linkage mechanisms with frictional revolute clearance joints is presented to investigate friction models' effect when surfaces collide with a non-zero tangential velocity. Unlike the smooth crank input mechanism, a double rocker four-bar linkage mechanism is analysed as a challenging problem in the impact mode. Resolving this concern, the novel friction model avoids discontinuity at zero velocity considering the accurate static friction zone. The results reveal that the novel friction model, compared with the piecewise friction model, is more effective in reflecting the mechanical systems' dynamic behaviour. In order to grasp the nonlinear characteristics of the high-speed four-bar linkage mechanism with our model in joint clearance, the Poincaré portrait, and Fast Fourier transformation plot are employed. It is proved that chaos exists in the dynamic response with the influence of the restitution coefficients and kinetic coefficient of friction.

Rolling Biped Polynomial Motion Planning

This work discloses a kinematic control model to describe the geometry of motion of a two-wheeled biped’s limbs. Limb structure is based on a four-bar linkage useful to alleviate damping motion during self-balance. The robot self-balancing kinematics geometry combines with user-customized polynomial vector fields. The vector fields generate safe reference trajectories. Further, the robot is forced to track the reference path by a model-based time-variant recursive controller. The proposed formulation showed effectiveness and reliable performance through numerical simulations.

A regularization method for solving dynamic problems with singular configuration

In the simulation process for multi-body systems, the generated redundant constraints will result in ill-conditioned dynamic equations, which are not good for stable simulations when the system motion proceeds near a singular configuration. In order to overcome the singularity problems, the paper presents a regularization method with an explicit expression based on Gauss principle, which does not need to eliminate the constraint violation after each iteration step compared with the traditional methods. Then the effectiveness and stability are demonstrated through two numerical examples, a slider-crank mechanism and a planar four-bar linkage. Simulation results obtained with the proposed method are analyzed and compared with augmented Lagrangian formulation and the null space formulation in terms of constraints violation, drift mechanical energy and computational efficiency, which shows that the proposed method is suitable to perform efficient and stable dynamic simulations for multi-body systems with singular configurations.

Force analysis of minimal self-adaptive fingers using variations of four-bar linkages

This paper presents the design and optimization of four versions of self-adaptive, a.k.a. underactuated, fingers based on four-bar linkages. These fingers are designed to be attached to and used with the same standard translational grippers as one finds in the manufacturing and packaging industries. This paper aims at showing self-adaptive fingers as simply as possible and analysing the resulting trade-off between complexity and performance. To achieve this objective, the simplest closed-loop 1 degree-of-freedom (DOF) linkage, namely the four-bar linkage, is used to build these fingers. However, it should be pointed out that if this work does consider a single four-bar linkage as the basic building block of the fingers, four variations of this four-bar linkage are actually discussed, including some with a prismatic joint. The ultimate purpose of this work is to evaluate whether the simplest linkages for adaptive fingers can produce the same level of performance in terms of grasp forces as more complex designs. To this end, a kinetostatic analysis of the four fingers is first presented. Then, the fingers are all numerically optimized considering various force-based metrics, and results are presented. Finally, these results are analysed and prototypes shown.

Hydrodynamics modeling of a piezoelectric micro-robotic fish with double caudal fins

An analytical hydrodynamics model for a piezoelectric micro-robotic fish with double caudal fins is presented in this paper. The relation between displacement of the piezoelectric actuator and oscillating angle of the caudal fin is established based on the analysis of the flexible four-bar linkage transmission. The hydrodynamics of caudal fins are described by airfoil and blade element theories. Furthermore, the dynamics and kinetics of the whole micro-robotic fish are analyzed and validated by experiments.

Design, Fabrication, Testing and Simulation of a Rotary Double Comb Drives Actuated Microgripper

This paper presents the development of a new microgripper actuated by means of rotary-comb drives equipped with two cooperating fingers arrays. The microsystem presents eight CSFH flexures (Conjugate Surface Flexure Hinge) that allow the designer to assign a prescribed motion to the gripping tips. In fact, the adoption of multiple CSFHs gives rise to the possibility of embedding quite a complex mechanical structure and, therefore, increasing the number of design parameters. For the case under study, a double four-bar linkage in a mirroring configuration was adopted. The presented microgripper has been fabricated by using a hard metal mask on a Silicon-on-Insulator (SOI) wafer, subject to DRIE (Deep Reactive Ion Etching) process, with a vapor releasing final stage. Some prototypes have been obtained and then tested in a lab. Finally, the experimental results have been used in order to assess simulation tools that can be used to minimize the amount of expensive equipment in operational environments.

Locomotion Identification Method of one-DOF Six-Bar for Jumping Robot

Exploring the locomotion of creatures is a challenging task in bionic robots, and the existing iterative design methods are mainly based on one or two characteristics to optimize robots. However, it is hard to obtain other features. Here, we introduced the thinking of system identification theory to the bionic robots, averting the exploration of the dynamics and reducing the difficulty of design greatly. A one-DOF six-bar mechanism (Watt I) was designated as the model to be identified, and it was divided into two parts, i.e. a one-DOF four-bar linkage and a three-DOF series arm. Then we formed constraints and a loss function. The parameters of the model were identified based on the kinematic data of a marmoset jumping. As a result, we obtained the desired model. Then, a prototype derived from the model was fabricated, and the experiments verified the effectiveness of the method. Our method also can be applied to other motion simulation scenarios.

High-capacity stacking apparatus for thermoforming machine – Part II: Structural design of the adjustable stacker driving mechanism

Part II presents the structural design of a high-capacity adjustable stacker mechanism for thermoforming machines which enables the receival, transport and stacking of cup-like products. It was previously established (please see Part I) that a four-bar linkage mechanism with a one-way clutch is the optimal solution for realizing the intermittent motion of the stacker conveyor. The main objective here is to enable the change of the stacker work parameters, with the goal of changing and adjusting the work stroke of the conveyor. Accordingly, there are two main requirements the solution needs to fulfill. The first is that of the regulation characteristic’s function – the relationship between the change of the work stroke and the change of the regulation parameter, must be linear, and the second is that it allows for regulation within a wide range. Due to this, the adopted solution proposed that two links have variable lengths. The input link should have discreet length values which correspond to different values of the conveyor work stroke, while the output link length should be continuously variable, within a narrow range thus ensuring linear regulation characteristic. Finally, it should be noted that this solution makes the stacker compatible with a wide array of products, which increases the productivity and flexibility, adjusting the stacker to receive a different product can be done quickly and easily and avoiding a halt in the production as it takes less time to adjust the stacker than the thermoforming machine.

Empirical Study of Constraint-Handling Techniques in the Optimal Synthesis of Mechanisms for Rehabilitation

Currently, rehabilitation systems with closed kinematic chain mechanisms are low-cost alternatives for treatment and health care. In designing these systems, the dimensional synthesis is commonly stated as a constrained optimization problem to achieve repetitive rehabilitation movements, and metaheuristic algorithms for constrained problems are promising methods for searching solutions in the complex search space. The Constraint Handling Techniques (CHTs) in metaheuristic algorithms have different capacities to explore and exploit the search space. However, the study of the relationship in the CHT performance of the mechanism dimensional synthesis for rehabilitation systems has not been addressed, resulting in an important gap in the literature of such problems. In this paper, we present a comparative empirical study to investigate the influence of four CHTs (penalty function, feasibility rules, stochastic-ranking, and ϵ-constraint) on the performance of ten representative algorithms that have been reported in the literature for solving mechanism synthesis for rehabilitation (four-bar linkage, eight-bar linkage, and cam-linkage mechanisms). The study involves analysis of the overall performance, six performance metrics, and evaluation of the obtained mechanism. This identified that feasibility rules usually led to efficient optimization for most analyzed algorithms and presented more consistency of the obtained results in these kinds of problems.

Stiffness compensation through matching buckling loads in a compliant four-bar mechanism

In this paper a novel alternative method of stiffness compensation in buckled mechanisms is investigated. This method involves the use of critical load matching, i.e. matching the first two buckling loads of a mechanism. An analytical simply supported four-bar linkage model consisting of three rigid links and four torsion springs in the joints is proposed for the analysis of this method. It is found that the first two buckling loads are exactly equal when the two outer springs are three times stiffer than the two inner springs. The force-deflection characteristic of this linkage architecture showed statically balanced behavior in both symmetric and asymmetric actuation. Using modal analysis, it was shown that the sum of the decomposed strain energy per buckling mode is constant throughout the motion range for this architecture. An equivalent lumped-compliant four-bar mechanism is designed; finite element and experimental analysis showed near zero actuation forces, verifying that critical load matching may be used to achieve significant stiffness compensation in buckled mechanisms.