The paper presents a simple and effective kinematic model and methodology to assess and evaluate the extent of the position uncertainty caused by joint clearances for multiple-loop linkage and manipulators connected with revolute or prismatic pairs. The model is derived and explained with geometric rigor based on Ting's rotatability laws. The significant contributions include (1) the clearance link model for a P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearances from the input error, (2) the generality of the method, which is effective for multiloop linkages and parallel manipulators, and (3) settling the dispute on the position uncertainty effect to parallel and serial robots due to joint clearance. The discussion is illustrated and carried out through symmetrically configured planar 8 bar parallel robots. It is found that at a target position, the uncertainty region of a three degrees-of-freedom (DOF) three-leg parallel robot is enclosed by a hexagon with curve edges, while that of its serial counterpart is enclosed by a circle included in the hexagon. A numerical example is presented. The finding and proof, though only based on three-leg planar 8 bar parallel robots, may have a wider implication suggesting that based on the kinematic effect of joint clearance, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in not only parallel robots but also single-DOF linkages cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

Nine-link type double-toggle mold/die clamping mechanisms are widely used in modern injection molding machines and die casting machines in order to provide sufficient mold/die clamping force for counteracting the pressure occurred inside molds/dies. In this paper, the analysis and experimental evaluation of mechanical errors in nine-link type double-toggle mold/die clamping mechanisms are presented. The kinematic error equations of the output link (i.e., the moving platen) caused by dimensional errors (or tolerances) of link members are derived analytically through the concept of tolerance sensitivity analysis. Evaluation indices based on the asymmetry of the mold/die clamping mechanism caused by mechanical errors are established. A case study is then given to demonstrate the derived analytical equations and the established evaluation indices. Subsequently, a prototype for performing the experimental evaluation is conceptually designed and was actually constructed. Experiments were conducted for evaluating the quantitative influence of mechanical errors on the operating performance of the constructed mold/die clamping mechanism. According to the experimental results, response surface modelling for benefiting the constructed mold/die clamping mechanism with better operating performance could be performed. The presented research results will be helpful in the tolerance analysis and mechanical error detection of nine-link type double-toggle mold/die clamping mechanisms.

We reveal the hindwing kinematics of a damselfly that are optimal for the thrust efficiency, which is a major concern of a bio-inspired micro-aerial vehicle. The parameters of the hindwing kinematics include stroke-plane angle, rotational duration, and wing phase. We developed a numerical self-propulsion model to investigate the thrust efficiency. The correlation analysis and optimal analysis were used to investigate the relation between varied hindwing kinematics and thrust efficiency. The results show that the optimal wing kinematics of the hindwing occur at a large stroke-plane angle and a small rotational duration in which the thrust efficiency might increase up to 22% compared with the original motion of the hindwing. The stroke-plane angle is highly positively correlated with thrust efficiency, whereas the rotational duration is moderately negatively correlated; the wing phase has the least correlation. The flow-field analysis indicates that a large stroke-plane angle combined with a small rotational duration has a weak forewing–hindwing interaction, generating a small resulting force on the hindwing, but the force comprises a small negative horizontal force, which hence increases the thrust efficiency. In a flight strategy for a micro-aerial vehicle, a large stroke-plane angle combined with a small rotational duration yields an optimal thrust efficiency, which is suitable for a flight of long duration. A small stroke-plane angle combined with a large rotation is suitable for hovering flight because it leads to a large negative horizontal force and a small vertical force. This work hence provides insight into the design of a tandem-wing micro-aerial vehicle.

The effect of wing shape on a forward-flying butterfly via decoupled factors of the wing-swept angle and the aspect ratio (AR) was investigated numerically. The wing-shape effect is a major concern in the design of a microaerial vehicle (MAV). In nature, the wing of a butterfly consists of partially overlapping forewing and hindwing; when the forewing sweeps forward or backward relative to the hindwing, the wing-swept angle and the AR of the entire wing simultaneously change. The effects of the wing-swept angle and AR on aerodynamics are coupled. To decouple their effects, we established wing-shape models with varied combinations of the wing-swept angle and AR based on the experimental measurement of two butterfly species (Papilio polytes and Kallima inachus) and developed a numerical simulation for analysis. In each model, the forewing and hindwing overlapped partially, constructing a single wing. Across the models, the wing-swept angle and AR of these single wings varied sequentially. The results show that, through our models, the effects of the wing-swept angle and AR were decoupled; both have distinct flow mechanisms and aerodynamic force trends and are consistent in the two butterfly species. For a fixed AR, a backward-swept wing increases lift and drag because of the enhanced attachment of the leading-edge vortex with increased strength of the wingtip vortex and the spanwise flow. For a fixed wing-swept angle, a small AR wing increases lift and decreases drag because of the large region of low pressure downstream and the wake-capture effect. Coupling these effects, the largest lift-to-drag ratio occurs for a forward-swept wing with the smallest AR. These results indicate that, in a flapping forward flight, sweeping a forewing forward relative to a hindwing is suitable for cruising. The flow mechanisms and decoupled and coupled effects of the wing-swept angle and the AR presented in this paper provide insight into the flight of a butterfly and the design of a MAV.