Design of flexure revolute joint based on compliance and stiffness ellipsoids

In view of the problems of low accuracy, small rotational angle, and large impact caused by flexure joints during the deployment process, an integrated flexure revolute (FR) joint for folding mechanisms was designed. The design was based on the method of compliance and stiffness ellipsoids, using a compliant dyad building block as its flexible unit. Using the single-point synthesis method, the parameterized model of the flexible unit was established to achieve a reasonable allocation of flexibility in different directions. Based on the single-parameter error analysis, two error models were established to evaluate the designed flexure joint. The rotational stiffness, the translational stiffness, and the maximum rotational angle of the joints were analyzed by nonlinear finite element analyses. The rotational angle of one joint can reach 25.5° in one direction. The rotational angle of the series FR joint can achieve 50° in one direction. Experiments on single and series flexure joints were carried out to verify the correctness of the design and analysis of the flexure joint.

Design, static analysis and development of a new three-legged shake table

In this paper, an alternative design is proposed based on a family of three-legged manipulators. Such manipulators have two actuators (one vertical and one horizontal) in each leg, unlike the standard UP̅S Stewart platform, which has one actuator in each leg. The arrangement of the two actuators is such a way that, to have vertical motion of the shake table only the Vertical Motion Actuators (VMA) are actuated and for longitudinal or lateral motion, the Horizontal Motion Actuators (HMA) alone are moved. Due to its inherent features such as simplified kinematics, control and distributed loading, a study is carried out to determine the performance of such three-legged manipulators as a shake table. Sinusoidal motion and white noise motions are given to the actuators and shown that the VMA forces have linear relationship with the platform forces. The translational stiffness and the torsional stiffness are studied separately for the manipulators. In the dynamic analysis, it is highlighted that the gravity load of the legs is borne by the Vertical actuators, irrespective of the motion being spatial or planar. Hence, this topology provides scope for lighter electromechanical actuation. The performance analysis of the 3 legged configuration is accomplished using simulation results, in comparison to a 7-UP̅S configuration of shake table. A prototype of the shake table is fabricated and tested with earthquake data of El Centro.

Design of a parallel compliance device with variable stiffness

This paper presents a parallel compliance device with variable translational stiffness properties. The variation of endpoint stiffness depends on the change of the spring stiffness in each limb. A synthesis algorithm for realizing the desired force compliance performance is built. Based on the proposed algorithm, a group of optimal spring stiffness can be derived. For the implementation of this device, an electromagnetic linear spring with current-controlled stiffness is developed. After testing the mechanical characteristics of the electromagnetic spring, a prototype of the parallel compliance device is built. The endpoint stiffness under different combinations of spring stiffness values is exhibited in the form of stiffness ellipsoids. A case is studied and verifies the ability of the presented compliance device to realize the desired endpoint stiffness. As the stiffness adjustment range of electromagnetic spring is limited, the bound of physically realizable stiffness of the presented compliance device is also discussed.

Interactions and Optimizations Analysis between Stiffness and Workspace of 3-UPU Robotic Mechanism

The interactions between stiffness and workspace performances are studied. The stiffness in x, y and z directions as well as the workspace of a 3-UPU mechanism are studied and optimized. The stiffness of the robotic system in every single moveable direction is measured and analyzed, and it is observed that in the case where one tries to make the x and y translational stiffness larger, the z directional stiffness will be reduced, i.e. the x and y translational stiffness contradicts with the one in z direction. Subsequently, the objective functions for the summation of the x and y translational stiffness and z directional stiffness are established and they are being optimized simultaneously. However, we later found that these two objectives are not in the same scale; a normalization of the objectives is thus taken into consideration. Meanwhile, the robotic system’s workspace is studied and optimized. Through comparing the stiffness landscape and the workspace volume landscape, it is also observed that the z translational stiffness shows the same changing tendency with the workspace volume’s changing tendency while the x and y translational stiffness shows the opposite changing tendency compared to the workspace volume’s. Via employing the Pareto front theory and differential evolution, the summation of the x and y translational stiffness and the volume of the workspace are being simultaneously optimized. Finally, the mechanism is employed to synthesize an exercise-walking machine for stroke patients.

Calculating Individual and Total Muscular Translational Stiffness: A Knee Example

Research suggests that the knee joint may be dependent on an individual muscle's translational stiffness (KT) of the surrounding musculature to prevent or compensate for ligament tearing. Our primary goal was to develop an equation that calculates KT. We successfully derived such an equation that requires as input: a muscle's coordinates, force, and stiffness acting along its line of action. This equation can also be used to estimate the total joint muscular KT, in three orthogonal axes (AP: anterior-posterior; SI: superior-inferior; ML: medial-lateral), by summating individual muscle KT contributions for each axis. We then compared the estimates of our equation, using a commonly used knee model as input, to experimental data. Our total muscular KT predictions (44.0 N/mm), along the anterior/posterior axis (AP), matched the experimental data (52.2 N/mm) and was well within the expected variability (22.6 N/mm). We then estimated the total and individual muscular KT in two postures (0 deg and 90 deg of knee flexion), with muscles mathematically set to full activation. For both postures, total muscular KT was greatest along the SI-axis. The extensors provided the greatest KT for each posture and axis. Finally, we performed a sensitivity analysis to explore the influence of each input on the equation. It was found that pennation angle had the largest effect on SI KT, while muscle line of action coordinates largely influenced AP and ML muscular KT. This equation can be easily embedded within biomechanical models to calculate the individual and total muscular KT for any joint.

Functional Analysis of Bushing in Four-Link Suspension on K&C Characteristics Using Multibody Dynamics Method

The link of multilink suspension usually has bushings at both body connection and wheel carrier connection. These bushings are designed subjected to the function of link. In the studies of vehicle dynamics, bushing could be represented by three translational stiffness and three torsional stiffness as well as corresponding damping. Due to specific location and orientation of each bushing, usually only one of these six stiffness plays an important role. In this paper, effect of bushing on suspension K&C characteristics was investigated with a four-link suspension. Through virtual loading tests, force distribution of suspension bushing was studied to find the relation between bushing stiffness and K&C characteristics. In order to quantitatively measure effect of bushing stiffness on parasitic rate, an “equivalent force” method based on energy conservation was proposed. Similarly, an “equivalent displacement” method was proposed to measure effect of bushing stiffness on suspension compliance. According to theoretical analysis and numerical calculation result, six stiffness of a bushing could be classified into three categories: main function stiffness closely related to suspension behavior, sub-function stiffness affecting parasitic rate or subjected to large load and non-function stiffness to be controlled within an acceptable range.

Stiffness Evaluation of Machines and Robots: Minimum Collinear Stiffness Value Approach

New stiffness performance indices using the collinear stiffness value (CSV) associated with a given configuration of the machine are proposed. The minimal CSV (MinCSV) is applied to stiffness evaluation for all types of configurations. Similar to the determinant, the MinCSV equals zero in singular configurations. In regular configurations, the MinCSV is applied to evaluation of local stiffness for a given configuration and global stiffness in the workspace, wherein stiffness limitations are satisfied. A screw stiffness value, i.e., the CSV during a screw displacement, presents the general case of the CSV. There are two important special cases: rotational and translational stiffness values. Procedures for evaluation of the MinCSV are developed in natural and dimensionless forms. The CSV of the hexapod are simulated and compared with those of serial-type mechanisms. The proposed approach presents an effective design tool for evaluation and limitation of stiffness of machines and robots.