Silicon-based soft parallel robots 4D printing and multiphysics analysis

4D printing soft robots guided by machine learning and finite element models

Parallel manipulators have been proposed to overcome accuracy problem in the end effector positioning, exhibited by serial manipulators(Stewart, 1965)(Reboulet, 1988)(Merlet, 2000). These parallel robots are primarly used in the applications for which the considered processes require a high degree of accuracy, high speeds or accelerations. Aircraft simulator (Stewart, 1965), machining tools (Neugebauer et al., 1998)(Poignet et al., 2002), and various other medical applications (Merlet, 2002)(Leroy et al., 2003)(Plitea et al., 2008) constitute some of the many possible applications of parallel robots. The computation of the inverse dynamic model is essential for an effective robot control. In the field of parallel robots, many approaches have been developed for efficient computation of the inverse dynamics. The formalism of d’Alembert has been used to obtain an analytical expression of the dynamics model (Fichter, 1986)(Nakamura & Ghodoussi, 1989). The principle of virtual works has been applied in (Tsai, 2000) for solving the inverse dynamics of the Gough-Stewart platform and in (Zhu et al., 2005) for a Tau parallel robot. Lagrangian formalism is applied in (Leroy et al., 2003) for the dynamics modeling of a parallel robot used as a haptic interface for a surgical simulator. These various approaches do not seem effective for a robot dynamic control under the real time constraint. A better computational efficiency can be achieved by the development of approaches using recursive schemes, in particular, based on the Newton-Euler formulation. Gosselin (Gosselin, 1996) proposed an approach for the computation of the inverse dynamic model of planar and spatial parallel robots, in which all the masses and inertias are taken into account. This proposed method is difficult to generalize for all the parallel architectures. Dasgupda et al (Dasgupta & Choudhury, 1999) applied this method to several parallel manipulators. Khan (Khan, 2005) has developed a recursive algorithm for the inverse dynamics. This method is applied to a 3R planar parallel robot. Bi et al (Bi & Lang, 2006) use the Newton-Euler recursive scheme for the computation of the articular forces of a tripod system. Khalil et al (Khalil & Guegan, 2004) proposed a general method for the inverse and direct dynamic model computation of parallel robots, which is applied to several parallel manipulators (Khalil & Ibrahim, 2007). Despite the large amount of contributions in this field, there is still a need for improving the computational effeciency of the inverse kinematic and dynamic model clculation for real-time control. In this paper, a parallel robot is considered as a multi robot system with 17

More than 130,000 people have strokes each year in the United States [1]. Of these victims, 76% are left with disabilities that cost the nation over $54 billion in lost work and medical fees. One prominent disability is upper extremity hemiplegia, which occurs among approximately 50% of stroke sufferers [2]. Robotic technology has the potential to provide an automated platform for controlled rehabilitation and assisted, task-oriented therapy. Several systems have been designed to assist in patient articulation of an impaired hand using rigid robotic components. While these products have been successful in articulating the pure bending motions of the four fingers, the limited capabilities of rigid technologies fail to reproduce the complicated motion path [5] of the thumb during opposition grasp (see Figure 1). This is the most important articulation for normal hand function and specifically for picking up everyday objects. To date, robotic systems for thumb rehabilitation have not been widely investigated [3] apart from some recent work [4] that used a multi-joint rigid robot.

Stroke and spinal cord injury are the main causes of lower limb impairments which require rehabilitation either in the early, middle or late stage. Lying and sitting patient postures are suitable for the early bedridden rehabilitation stage where the patient is too weak to support his weight. In this paper, a novel 3 DOFs planar parallel manipulator-based lower limb rehabilitation robot in the lying posture is developed to achieve leg continuous passive motion, straight leg raise and straight leg side raise as well as cycling exercises for bedridden patients. The proposed robot is based on a non-conventional structure planar parallel manipulator with three different kinematic structure limbs; namely two RPR limbs and one RRR limb. It has straight line shape moving platform. For a certain position of the moving platform achieved by actuating the prismatic joints of the two RPR limbs, the RRR limb with the straight line shape moving platform constitute a parallelogram 4-bar mechanism that can achieve the full cycle orientation of the moving platform. This structure provides partially decoupled motion for the position and orientation and singularity free large dexterous workspace with unlimited orientation capability suitable for cycling motion. The kinematic analyses are carried out to prove those advantages.

The objective of this paper is to determine whether a planar parallel manipulator with redundant actuation has better tracking accuracy than a planar parallel manipulator without redundant actuation. The effects of the redundant actuation on tracking accuracy of parallel manipulators are studied by using two different experimental platforms. The first platform is the planar five-bar parallel manipulator with normal actuation, and the other one is the planar parallel manipulator with redundant actuation. The dexterity pictures and the kinematic configurations of the two platforms validate the kinematic advantages from the redundant actuation. In order to study the dynamic advantages of the redundant actuation further, a nonlinear adaptive controller is presented for the two platforms. The experimental comparison is implemented on two actual parallel manipulator platforms, and from the experimental results, one can find the tracking accuracy of the parallel manipulator with redundant actuation can be improved above 38% than that of the five-bar parallel manipulator without redundant actuation.

The benefits of soft robotic actuation have been recognized and soft actuators are increasingly used. Soft robots are generally lightweight, inexpensive, and highly compliant. They are often used for interaction with small objects which only require relatively low force output. Nevertheless, large-scale applications can still benefit from the advantages of soft actuators if force output is sufficiently large. Some soft actuation has been employed in large-scale applications, but the area remains greatly underexplored. This article presents the Soft Torque-generating Actuation System (STAS) a lean soft actuation architecture capable of producing relatively large torque output while maintaining compliant interaction with the environment. Design and fabrication of the system are described, and a theoretical model is introduced for predicting torque output. The model is validated against measured torque output, and the system is further characterized in terms of power output. The model is shown to adequately predict torque output at low actuator angles. The system is shown to require only 30.0 kPa to achieve a large torque output of 10 N-m. The system also reaches a peak power output of 1.29 Watts. Finally, a versatile application of STAS is shown through a wearable joint-assistive device. The STAS is a promising architecture for a new type of high force actuation using soft actuators.

Soft robots are inherently compliant and adaptive, therefore they are promising candidates for interacting with humans. However robotic manipulators utilizing soft actuators are often constrained by a series of actuator performance limitations. In this work we design a novel linear soft robotic actuator with significantly improved performances over the existing products, achieving 300% deformation ratio, quasi-constant output force over a wide motion range, while maintaining passive compliance and adaptability. Moreover, the novel actuator is less prone to friction, and could be fabricated using inject molding and 3D printing, hence having high repeatability at very low cost. An analytical model was developed to characterize the actuator behavior and provide a guideline for actuator design according to performance specifications. A 6 DOF soft manipulator was designed and fabricated utilizing the novel soft actuator. The manipulator arm had a serial kinematic structure with a biomimetic wrist and was driven by 12 soft actuators mounted onto the arm links. With 1.2m workspace radius and 1kg payload, the working air pressure could be as low as 1bar. Preliminary results have shown the validity of the novel soft actuator and manipulator designs, as well as the strong potential of soft robots in human-oriented applications.

Continued technological progress in robotic systems has led to more applications where robots and humans operate in close proximity and even physical contact in some cases. Soft robots, which are made of highly compliant and deformable materials, provide inherent safety features unlike conventional robots that are made of stiff and rigid components. Soft robotics is a rapidly developing field exploiting biomimetic design principles, novel sensor and actuation concepts, and advanced manufacturing techniques. In this study, we propose novel 3D printable soft vacuum actuators that are inspired by the sporangium of fern trees. These actuators that are directly manufactured using commercial and affordable fused deposition modeling 3D printers offer many advantages such as high actuation speed (5.54 Hz), long lifetime (123,000 cycles), large payload to weight ratio (∼26), and significant output forces (∼16 N). The behavior of these actuators is accurately predicted, and their performance is optimized using finite element modeling. Furthermore, diverse robotic applications such as locomotion robots (a walking robot moving with an average forward speed of vf = 3.54 cm/s, and a hopping robot called Gongaroo hopping with an average speed of vf = 3.75 cm/s), grippers, and artificial muscles have been established and activated using the new soft actuation concept. Finally, to demonstrate the modularity of the proposed actuation concept, soft actuators with multiple degrees of freedom and variable length are established using a series of 3D printable vacuum hinges.

This paper addresses the kinematic and dynamic models of a 3-PPR parallel manipulator, which are the foundation of parallel manipulator dynamic control. Then, based on the Udwadia-Kalaba equation, a three-step procedure is exploited to realize the perfect trajectory tracking of 3-PPR parallel manipulator involving the known uncertainty. In addition, when the initial conditions are incompatible and system parameters are uncertain, we adopt the adaptive robust control method to realize approximate trajectory tracking of the planar parallel manipulator. The controller consists of three parts. The first part is the perfect control of dynamic model based on the Udwadia-Kalaba equation. The second part deals with the incompatibility of initial conditions. The third part is the robust control for system uncertainty regulated by adaptive law. Finally, on the basis of theoretical analysis, the adaptive robust control algorithm is demonstrated by simulation.

Emerging classes of soft robotics with flexible actuation, intelligent sensibility, and biomimetic functionality are driving significant advances in academic researches and commercial applications. Such new generation robotics relies heavily on important breakthroughs in soft matter engineering and flexible actuation systems. Unlike conventional rigid robots, soft robots generally have unique sporting styles and manufacturing strategies. Recently, a series of newly developed soft materials—gallium‐based liquid metals (LMs) are found to display dramatical roles in making soft machines and robotics with their unusual properties in soft robotic actuation and self‐driven field. With superior merits of both high stretchability and electroconductivity over conventional soft materials, LM is increasingly innovated as flexible sensors and actuators in constructing intelligent soft robots. Typical advances in LM enabled soft machines and robotics are summarized and interpreted, herein, with special focus on the driving principles of the LM objects, the preparation methods of LM flexible electronics for making soft robots, and the applications of LM in biomedicines and intelligent robots, together with the consideration of key challenges facing LM‐based soft robotics and its future prospects.

In the design of a mechanism, the quality of effort transmission is a key issue. Traditionally, the effort transmissivity of a mechanism is defined as the quantitative measure of the power flowing effectiveness from the input link(s) to the output link(s). Many researchers have focused their work on the study of the effort transmission in mechanisms and diverse indices have been defined. However, the developed indices have exclusively dealt with the studies of the ratio between the input and output powers and they do not seem to have been devoted to the studies of the admissible reactions in passive joints. However, the observations show that it is possible for a mechanism to reach positions in which the transmission indices will have admissible values but the reaction(s) in passive joint(s) can reach excessively high values leading to the breakdown of the mechanism. In the present paper, a method is developed to ensure the admissible values of reactions in passive joints of planar parallel manipulators. It is shown that the increase of reactions in passive joints of a planar parallel manipulator depends not only on the transmission angle but also on the position of the instantaneous center of rotation of the platform. It allows the determination of the maximal reachable workspace of planar parallel manipulators taking into account the admissible reactions in its passive joints. The suggested method is illustrated via a 5R planar parallel mechanism and a planar 3-RPR parallel manipulator.

Four-dimensional (4D) printing technology, as a next-generation additive manufacturing method, enables printed objects to further change their shapes, functionalities, or properties upon exposure to external stimuli. The 4D printing of programmable and deformable materials such as thermo-responsive shape-memory polymers (trSMPs), which possess the ability to change shape by exposure to heat, has attracted particular interest in recent years. Three-dimensional objects based on SMPs have been proposed for various potential applications in different fields, including soft robotics, smart actuators, biomedical and electronics. To enable the manufacturing of complex multifunctional 3D objects, SMPs are often coupled with other functional polymers or fillers during or before the 3D printing process. This review highlights the 4D printing of state-of-the-art multi-component SMP formulations. Commonly used 4D printing technologies such as material extrusion techniques including fused filament fabrication (FFF) and direct ink writing (DIW), as well as vat photopolymerization techniques such as stereolithography (SLA), digital light processing (DLP), and multi-photon polymerization (MPP), are discussed. Different multicomponent SMP systems, their actuation methods, and potential applications of the 3D printed objects are reviewed. Finally, current challenges and prospects for 4D printing technology are summarized.

Four-dimensional (4D) printing, an evolution of additive manufacturing (AM), integrates stimuli-responsive materials like thermal-induced shape memory polymers (TSMPs) to enable programmable, time-dependent transformations in structures. This review systematically examines recent advancements in TSMPs, 4D printing technologies, and fabrication strategies, emphasizing their interdisciplinary convergence and applications. TSMPs, with their unique phase-separated microstructures, modulus disparity, and tailorable recovery behaviors, form the foundation of 4D-printed systems, enabling innovations in aerospace, healthcare, and soft robotics [1–3, 33–45]. Key printing methods—including fused deposition modeling (FDM), direct ink writing (DIW), PolyJet, stereolithography (SLA), and digital light processing (DLP)—are analyzed for their strengths and limitations. FDM dominates due to cost-effectiveness but faces challenges in resolution and anisotropy [88, 91–93], while SLA and DLP offer high precision and speed but require material optimization [105, 111–115]. Advanced fabrication strategies, such as localized TSMP printing, composite reinforcement with carbon nanotubes or Fe 3O 4 particles, and sacrificial mold templating, expand design possibilities for multi-functional and multi-scale structures [117–120, 140–144]. Despite progress, challenges persist, including environmental sensitivity of TSMPs, interlayer bonding in AM, and dynamic modeling of non-equilibrium thermal responses [74, 77, 146]. Future directions focus on multi-responsive materials, machine learning-driven constitutive models, and sustainable bio-based formulations to address scalability and cyclic durability [31, 77, 147–149]. By bridging material science, computational modeling, and advanced manufacturing, this work provides a roadmap for harnessing 4D-printed TSMPs in real-world applications, from self-deploying biomedical devices to adaptive aerospace systems [28, 85, 137].

Geometric isotropy indices for workspace analysis of parallel manipulators

Conventional robots are constructed with rigid parts and materials, restricting their ability to deform freely and adapt to the external environment. Performing tasks such as handling delicate materials and navigating narrow pathways is challenging for these typical robots made of stiff materials. However, there is a growing demand for such functions in various industries. Recent advances in soft robotics have garnered considerable attention as solutions to these challenges. Soft robotic systems in various forms present a systematic solution for performing unique tasks. The goal of soft robotics research is to develop advanced technologies, incorporating innovative robotic mechanisms based on soft materials and structures to enhance adaptability. Soft robots find broad applications in diverse fields, including industry, healthcare, and field exploration. Soft component technology plays a crucial role in configuring soft robots. Soft actuators introduce new types of motion and operation mechanisms, while soft sensors measure the deformation of the actuators with a tiny stiffness change. These advancements in soft actuators and sensors encourage researchers to explore new robotic designs and applications. Additionally, the component technology enables the integration of soft and typical robots into hybrid B Youngsu Cha