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The highly mathematical nature of introductory level vibrations and control theory courses results in students struggling to understand the concepts. Hands-on activity demonstrated in class can help them better understand the concepts. However, there is still an ongoing effort to lower the currently substantial cost of educational laboratory equipment for undergraduate-level engineering courses. Also, with the COVID-19 crisis, the Spring 2020 academic year took an unexpected turn for academics and students all over the world. Engineering faculty who teach laboratories had to move online and instruct from home. Online course preparation takes more time and effort compared to traditionally designed face-to-face courses and was compounded considering the unprecedented situation where many instructors didn't have time to record data from existing lab equipment or record video in their laboratories. In this paper, we present a Matlab Simscape GUI program designed to simulate modeling and control of dynamical systems for vibrations and control theory courses, and their associated laboratories, as one potential solution for online instruction. To complement the simulation program, online classroom and homework activities were designed using a learning sciences approach connecting several critical educational theories which can bolster student motivation, engagement with the material, and overall learning performance. The simulation is presented along with data from 19 students who completed the associated classroom and homework activities. Survey results probing student perceptions about the value of the learning tasks for the simulation were overwhelmingly positive and indicate this approach holds promise in supporting student learning.

This paper reports on the design, fabrication, and evaluation of a novel 3D printed vacuum based soft sensor and its application as hand motion sensor. Soft sensors are an integral part of soft robotics as an emerging field of science that enables safe and easy human to machine interaction. The conventional sensors used to interface with humans in robotic systems are mechanically incompliant. Because of this mechanical compliance mismatch, these sensors cause unsafe interactions with humans. Recent advancements in 3D printing technology have allowed fabrication of complex geometries with soft polymers, perfect for more delicate and user-friendly sensors. While the existing soft pneumatic sensors work based on the positive pressure due to deformation, the proposed sensor in this work works based on vacuum due to deformation. In comparison with the similar positive pressure sensor, our vacuum-based sensor is much softer and has minimum interference with hand motion. Finite element analysis (FEA) is used to analyze the design. Also, a kinematic model of the hand is developed using Matlab to visualize the hand motion based on the sensor data. This could show the potential application of the soft hand motion sensor in virtual reality and telehealth.

This study presents the design, development, and experimental testing of a single piece designed compliant gripper manipulated by a 3 DOF soft robot. The manipulator consists of two soft links. While the bottom arm is 2 DOF and is tendon driven by two servo motors, the SDOF upper arm is also tendon driven by a servo motor. The two-finger-designed compliant gripper is also actuated by a servo motor. The base of the robot holds the motors and the soft manipulator. The MATLAB Simscape model of the robot is created to perform deformation and motion analysis of the gripper and soft manipulator. The cad model of the robot is imported, and the manipulator parts are converted into soft links using discrete beam elements. The large deflecting hinges on the compliant grippers are also transformed to mimic the physical gripper. Since the soft manipulator and the compliant gripper were designed monolithically, the robot was 3D printed as a single piece using thermoplastic polyurethane (TPU). The gripper is tested for its grasping and lifting performance while recording the applied forces by the gripper using a Flex sensor. Using the opencv tool for image processing and object analysis, we used a dual-camera setup with a known environment to add intelligence to the robot. Since the manipulator is designed as soft, the gripper can reach any position within its working space with any orientation.

Despite the advantages and superiorities of compliant mechanisms and soft robots over rigid mechanisms, optimizing the stiffness of flexible links and dynamic properties of complex and high mobility designs is increasingly challenging. Additionally, the largest challenge in the design and modeling of such systems is understanding the deformation of the two bodies when connected along with their interaction in complex cases such as large deflecting buckling beams, especially for people who are new in the area. There exist several methods and techniques for obtaining kinematic relations as pseudo rigid body modeling (PRBM), first and second kind of Elliptica theory, discrete beam element method for simple geometries of compliant mechanisms, and nonlinear dynamical modeling of soft robots assuming using constant curvature spatial curves, and also machine learning. To address this issue, we present the user-friendly and open-access MATLAB Toolbox for the design and motion analysis of compliant mechanisms and soft robots. The developed toolbox serves as a platform to visualize the deformation of compliant joints and compliant beams (Module 1), visualize the displacement of various compliant mechanisms (Module 2), design simple and complex compliant mechanisms using the hinges and beams, and design and motion analysis of soft robots (Module 3).

Among the robotic systems, biomimetic robots performing fish-like locomotion have been the focus of much attention recently as there are many applications for swimming robots, including monitoring of underwater environments, detection of pollution, and disaster relief. This study presents the design and development of a biomimetic fish-like robot based on real carp locomotion. The robot has five main body parts including the head, soft neck, hinged body, compliant tail, and caudal fin. The head houses three ultrasonic sensors to guide the robot while connected to the body through two degrees of freedom (DOF) soft link resembling the neck vertebrate. The 2 DOF soft link enables the head to bend up, down, left, and right which is essential for controlling the soft robot’s direction. The body is connected to the soft tail using a quick return crank mechanism to actuate the tail. The tail integrates a soft tail and a rigid caudal fin. While all parts of the soft fish-like robot are 3D printed using polylactic acid (PLA), thermoplastic polyurethane (TPU), the mold is made from silicone rubber to waterproof. The ultrasonic sensors are utilized to detect obstacles so that the robot may maneuver around. The swimming pattern only for two-dimensional motion is tested in the air and underwater. According to the experimental results, the proposed robot better imitates the fish through its soft 2 DOF link and tail.

Limited resources available to the engineering faculty and students impede student learning and deep understanding of the material that is presented in the dynamics and mechanical vibrations courses. Active learning practices such as learning by doing is an effective way to not only build a solid foundation in knowledge but also help students develop engineering skills. However, these courses are mainly taught in a traditional manner and many students struggle in connecting the theory to its real-world application and lose interest. Although mechanical engineering students get more hands-on opportunities in the laboratories, they take vibrations and control laboratories in the following semesters since vibrations is a pre-requisite for these labs. To address this issue, we designed 3 low-cost, compact, and portable laboratory equipment and fabricated them using 3D printing technology. The first equipment is a 3-pendulum system with different lengths and tip loads that can be utilized in the engineering dynamics course. While the second equipment is a 2 DOF compliant vibration isolator consisting of flexible beams, masses, and a linear actuator, the third equipment is a non-linear cantilever beam to be utilized in the vibrations courses and their associated laboratories.

Soft parallel robots are among the latest advancements in the field of soft robotics with wide range of applications. Most of the existing soft robotic systems comprise from serial soft arms which can provide high degrees of freedom (DOF), but suffer from low stiffness, and limited payload due to their soft structure. To address these issues recently researchers have introduced soft parallel robots. Similar to their rigid counterparts, soft parallel robot will have higher blocking force, stiffness, and accuracy. We have previously introduced two, and three DOF soft parallel robots and in the current work we will introduce a novel six DOF robot named 3-universal-spherical-revolute (3USR) soft parallel robot. This robotic system is consisted of three closed-loop kinematic chains. Each chain includes a soft active arm with two DOF which is connected to a compliant passive link through soft joints. This configuration provides six DOF for the soft robot (x, y, z, roll, pitch, yaw). The prototype of the robot is 3D printed using NINJA flex, thermoplastic polyurethane (TPU), and polylactic acid (PLA). Each soft active arm consists of a two DOF tendon driven soft actuator which is 3D printed using NINJA flex and are actuated using two servo motors. Two types of soft joints are used namely soft spherical and revolute joints. The shape and size of the soft joints are optimized so that the robot will achieve six DOF. MATLAB Simscape model is used to simulate the dynamical response of the mechanism for various inputs.

The vast majority of undergraduate engineering students struggle to acquire a deep understanding of complex topics presented in mechanical vibrations and control theory courses due to their highly mathematical nature, limited resources on the use of commercially available turn-key laboratory equipment, and lack of innovative teaching tools to improve student understanding. In this study, we developed open-source standalone virtual laboratory exercises for vibrations and control theory courses using Matlab Simscape. The virtual labs enable students to change the system parameters, develop a feel of the material, and record and observe the system response through mechanics explorer.

This paper reports on Simscape modeling and experimental validation of compliant mechanisms and soft robotic systems. During the past decade, there has been a lot of advancements in terms of the development of novel soft robotic systems, actuators, and sensors. However, efficient modeling of these systems is still a challenge for researchers. This is due to the existence of nonlinearities such as large deformation in the structure of soft robotic systems and compliant mechanisms. While analytical models can be used for conventional rigid robots, the application of these models for soft robots is limited. Simscape is an efficient tool for modeling soft robotic systems and compliant mechanisms as it can take into account large deformation. To validate the developed Simscape models we used a 6 DOF electromagnetic position sensor for each of the example systems such as a compliant bistable mechanism, compliant linear actuator, and a soft Delta robot.

This study presents the design, analysis, dynamical modeling and control of a planar, flexure based closed chain compliant mechanism. Mechanism is designed as a single piece and comprised of rigid-flexure links connected in series. Base links of the mechanism can be actuated through two servo motors and translated along the horizontal direction using two step motors. Two servo motors are mounted on a rail-cart system and carts are equipped with belt drive to enable horizontal displacement. Dynamical model of the mechanism is derived by adapting pseudo rigid body modeling method, vector closure loop equations, Euler’s laws of motion and geometric constraints. Mechanism is 3D printed using thermoplastic polyurethane filament (TPU), motion of the mechanism is video recorded and position of the tip along with the motion of center of each links are captured using image processing. Mathematical model is simulated in Matlab Simulink and validated with the experimental data. A reference trajectory drawn within the workspace of the mechanism on iPad is successfully traced in real time using the simplified model, mirror imaging program and inverse kinematics. The proposed mechanism can be utilized as a haptic device and a compliant manipulator in industrial applications where high precision and larger workspace is desired.

Commercially available turn-key systems are expensive and require substantial lab space, making it harder to accommodate many in vibrations laboratories. This study presents a low-cost, compact, and portable torsional mechanism incorporating multiple rotating disks and a long thin rod supported vertically with bearings and fixed supports at the top and bottom ends to study the modeling of systems using experimental data. The mechanism consisting of a rod, disks, bearing, and disk supports, and the base is built by 3D printing using thermoplastic PETG. The long, thin rod in this mechanism serves as a torsional spring. The equivalent stiffnesses of the 2 DOF system can be changed by adjusting the vertical position of the disks with respect to the ends, thereby shortening or lengthening the effective twist length of the thin rod. The overall dimensions of the mechanism are 6 inches in height, 5 inches in width, and 2 inches in depth, and the expected cost including the experimental setup is around USD$30 if an Arduino is used for data acquisition and $170 if equipped with a National Instruments external data acquisition card. Learning objectives of the lab course utilizing the proposed mechanism are identified. The free response data are collected for a single degree-of-freedom system using an external data acquisition card and potentiometer and unknown parameters of the system are determined by system identification. Mechanism unknown parameters are calculated using system identification and a theoretical model is compared with the experimental data.

In this study, we present the design and development of a compliant multi-link hopping mechanism actuated by a single DC motor. Mechanism consists of torsional spring, two symmetrically arranged six bar mechanism connected through the bottom gears and a compliant preloaded pinned-pinned buckling beam serving as a nonlinear spring. Kinematic and dynamical analysis are performed using both Newtonian dynamics, vector closure loop equations and geometric constrains of the design to predict the motion of the mechanism. Adams simulations are performed to obtain the force-deflection curve for flexible beam and torque-angular displacement curve for flat spiral spring. Mechanism is built by 3D printing all parts using thermoplastic based polylactic acid PLA filament. Continuous hopping motion is created without requirement of any hydraulic and pneumatic actuators or mechanical springs to store and release energy during the complete motion. The actuator is connected to a 3D printed flat spiral spring to control the speed and pinned-pinned buckling beam is attached in between two symmetrical multi-link mechanism to increase the effect of impact.

Success of emerging field of soft robotics relies on the development of efficient soft actuators. Most of these actuators suffers from disadvantages such as limited blocking force, lifetime, high actuation voltage, and slow response time. Swimming robots in particular utilizes single or multiple soft actuators to mimic the dynamic of a fish during motion. In this study we used 3D printing to fabricate soft electromagnetic actuators based swimming robot. The mechanism consists of soft actuator legs, compliant paddle and floatation. We designed a hybrid propulsion mechanism by using double soft leg actuators as caudal fins and side paddles as pectoral fins. This increases the thrust and efficiency to overcome the water drag as well as providing stability. We 3D printed the soft actuator using thermoplastic polyurethane (TPU) filament to reduce the manufacturing cost as well as to simplify the process. The main body is also 3D printed using polylactic acid (PLA). The infill percentage of the soft body is adjusted to increase the bending performance without yielding under actuation. The prototype of the swimming robot was tested in water. The body velocity of the robot is measured as 0.106 BL/s. Motion analysis was made MSC Adams by simulating the deformation of flexible beams.

Biomimetic robots have been the focus of many studies for the last decades since the motion in nature is accomplished through the bending of the flexible arms once subjected to an input force, displacement or torque as opposed to their rigid body counterparts thereby increasing the workspace. This study presents the design, analysis, and modeling of a novel monolithically designed compliant mechanism. The mechanism consists of two translational springs, three sliding carts, housing for the two servo motors, and two rigid-flexure-rigid (RFR) arms. While the main body of the biomimetic robot can be 3D printed using polyethylene terephthalate glycol (PETG), the RFR links are 3D printed in thermoplastic polyurethane (TPU) to prevent yielding when loaded. The mechanism model is derived using D’Alembert’s principles, pseudo rigid body modeling, and kinematic constraints. Finite element analysis is performed in MSC Adams and simulation model outputs are validated through experimental data for forward motion.

This study presents a passive, self-actuated, 3D printed compliant knee joint for children in developing regions to decrease the overall expense of above knee prosthesis as well as increase the ease to print multiple prosthesis during their growing cycle. A single piece designed five-bar mechanism is proposed to provide adequate human-like gait instead of the traditional pegleg gait provided in previous rigid models. This gait is achieved through the use of both compliant links as well a novel 3D printed approach which is more accustomed to children because of the mechanism’s lightweight. In addition to the compliant knee joint, a compliant ankle possessing a flexure hinge placed at the toe is also designed to provide required bending during the gait cycle. The approach of using a fully passive knee joint enables to limit the weight of the prosthesis to create less of a burden to children and by isolating the need to utilize motors. A test bench consisted of a rack-pinion, two parallel rods, supports, and two servo motors are fabricated to experiment the performance of the knee joint. While the test bench is 3D printed using polylactic acid (PLA), the compliant knee joint is 3D printed in thermoplastic polyurethane (TPU) to emulate the gestures of a real human leg. Simulations are performed in Matlab Simscape to validate that the proposed knee joint mimics the human knee and desired angles.

Learning by doing has proven to have numerous advantages over traditionally taught courses in which the instructor teaches the topic while students remain passive learners with little engagement. Although laboratories give hands-on opportunities for undergraduate mechanical engineering students, they have to wait for a semester for the lab course for instance the prerequisite of the vibrations and control laboratory is the mechanical vibrations course. Since the nature of the dynamics branch consisted of dynamics, vibrations, and control theory courses are highly mathematical, students struggle comprehending the introduced topic and relate the theory to its real-world application area. Furthermore, it’s almost impossible for an instructor to bring the existing educational laboratory equipment to the class since they are bulky and heavy. The advents in manufacturing technology such as additive manufacturing bring us more opportunities to build complex systems new materials. This study presents the design, development, and implementation of low-cost, 3D printed vibratory mechanisms to be utilized in mechanical vibrations, control theory courses along with their associated laboratories. A pendulum, cantilever beam integrated with springs, and a rectilinear system consisted of two sliding carts, translational springs, and a scotch yoke mechanism are designed. The main parts of the mechanisms are 3D printed using polylactic acid (PLA), polyethylene terephthalate glycol (PETG), and thermoplastic polyurethane (TPU).

Students taking traditional undergraduate level engineering courses not only struggle with highly complex concepts but also struggle in linking the physical meaning of the derived mathematical equations. In this study, we developed a standalone and user-friendly Matlab Simscape Graphical User Interface (GUI) program to visualize the concepts presented in the undergraduate level helicopter dynamics course. The developed GUI program enables students to change the parameters of the blade including the rotor radius, blade chord, type of airfoil, material properties, the weight of the aircraft and analyze the effect of the parameter on the performance of the helicopter rotor. The program uses motion dynamics to simulate the blade movement in hover and forward flight. The Simspace GUI program is composed of four modules starting with a simplistic beam model. In the first module, the blade is considered as a simple cantilever beam where an input point load is applied at the tip of the blade either vertically down or at an angle. In the second module, the force is replaced by a radially distributed load that simulates lift distribution along the span of the blade. In the third module, the distributed load is applied to various types of airfoils ranging from symmetrical NACA airfoil to supercritical airfoils. In the fourth model, the sectional velocities vary as a function of azimuth, and the forward-moving rotor is simulated.

This study presents the design and development of a tendon-driven soft gripper manipulated by a 4 DOF robotic arm. The proposed robotic arm and gripper explore new areas focusing on increasing the grasping performance of the gripper as well as the workspace. The gripper is designed with 3 fingers and driven by tendons using two servo motors. The tension of the strings is adjusted using a pulley mechanism and a string. The opening and grasping of the soft gripper are accomplished by each motor. The wide opening allows the gripper to grasp larger objects. The parallel robotic arm motion is actuated using 4 motors. These motors are mounted on a spherical shoulder plate with attached circular plates with angled axles are. The axles are angled so that their axes of rotation converge to the center point of the shoulder plate. The vertical and lateral motion of the robotic arm is controlled by the series of radial linkages connected to the motors, with a parallel linkage attached to the radial linkages to actuate the forearm of the mechanism. The robotic arm is 3D printed in polylactic acid (PLA) and the monolithic soft gripper is 3D printed in thermoplastic polyurethane (TPU). The gripping force applied by the gripper is obtained using flexible sensors attached to the tip of the 3 fingers. The finite element analysis is performed in SoldWorks and the link lengths are optimized to trace the desired workspace. The mechanism is tested for its grasping and lifting of various objects showing promising superiorities in terms of its grasping capabilities mimicking the human hand. If the robotic arm is mounted on a moving platform, then it can serve as an assistive robot for the elderly.

Undergraduate mechanical engineering students struggle in comprehending the fundamentals presented in an introductory level mechanical vibrations course which eventually affects their performance in the posterior courses such as control theory. One salient factor to this is missing the visualization of the concept with hands-on learning since the vibrations and control laboratory course is offered in the following semester. This study presents the design, development of three portable and 3D-printed compliant vibratory mechanisms actuated by a linear motor and their implementation in vibrations course and vibrations and control laboratory. The proposed setups consist of flexible and compliant springs, sliders, and base support. Mechanisms are utilized to demonstrate free and forced vibrations, resonation, and design of a passive isolator. In addition to the 3D-printed, portable lab equipment, we created the Matlab Simscape GUI program of each setup so instructors can demonstrate the fundamentals in the classroom, assign homework, project, in-class activity or design laboratory.

As technology advances and enables us to design and realize complex systems using new materials and manufacturing methods, biologically inspired robots in every aspect of engineering have attracted much attention in the last few decades. This paper presents the design and motion analysis of monolithically designed two compliant swimming robots that are actuated and controlled by single motor. Each design incorporates large deflecting compliant members and rigid levers to transfer the input torque to the different parts on the mechanism. While the first design integrates flexible tail to perform swimming motion, the second design adopts snapping type motion for the same action. Both mechanisms are 3D printed and tested for forward motion. The first robot has a constant speed of 0.68 BL/s while the second has an average speed of 0.6 BL/s. Kinematic model using pseudo rigid body modeling (PRBM) is derived to calculate the load-deflection curves of the flexible tail for Design I, finite element analysis for deflection analysis are performed for Design II.

This paper presents the design, development, modeling and control of a biomimetic multi degree of freedom compliant locomotive mechanism that can follow a prescribed trajectory. The research objective of this study is the design of a high mobility and flexible planar locomotive mechanism incorporating large deflecting compliant hinges. The actuation is realized using servo motors. Mechanism is consisted of five sliding carts, rail, 3D-printed supplementary pieces to house motors and pins. Carts are connected by monolithically designed two arm links joined by a large deflecting flexure. Four servo motors are mounted on the driven carts. Since sliding carts are identical, forward motion is achieved by changing the friction of carts through the connecting pins. Dynamical model is created in Matlab Simulink using Euler’s laws of motion principle, pseudo rigid body modeling (PRBM), vector closure-loop equations and kinematic constraints. To robustly control the position of the mechanism, first its nonlinear dynamics replaced with a family of linear time invariant systems which have parameter uncertainty. Then a robust controller is designed based on the Quantitative Feedback Theory (QFT) for the desired robust tracking and stability bounds. QFT is one of the most powerful robust control techniques which can take into account both phase and magnitude information of the system and enables the designer to minimize the cost of feedback by clearly observing the design constraints through robust performance bounds. Finally, the performance of the designed controller is validated though nonlinear simulations using the nonlinear dynamics of the mechanism. It has been shown that the mechanism can consistently track the desired inputs both in frequency and time domains.

There is still a demand for compact, portable, low-cost laboratory equipment for undergraduate engineering students, since turn-key systems are expensive and require substantial lab space. We propose a novel compliant mechanism demonstrating the fundamentals of vibration control to undergraduate engineering students. The mechanism consists of a translational two-degrees-of-freedom system using initially straight fixed-free flexible beams connected to primary and secondary masses. A linear actuator is connected to the primary mass and two laser displacement sensors are utilized to record displacement of each mass. Primary and secondary mass displacements are controlled by adjusting the forcing frequency while keeping the amplitude constant. All parts of the mechanism are three-dimensional printed to reduce cost. The cost of the device itself is less than $5, and with the actuator and data acquisition the total cost is $1300. The mechanism was demonstrated to 32 undergraduate Machine Dynamics and Vibrations students divided into two course sections. Feedback on the student learning experience was collected using the Student Assessment of Learning Gains survey instrument. Results indicate positive overall feedback, with students highlighting the value of using MATLAB to control the system and analyze results, the connections to real-world applications incorporated into the learning activity, and the hands-on nature of the learning experience.

A partially compliant novel translational double dwell mechanism is presented in this article. The designed mechanism consists of initially straight and preloaded pinned-pinned compliant links, rigid crank, slider-rail system and a DC motor. Slider doesn’t move until the critical buckling load is achieved and then snaps to its maximum and returns back to initial position as the crank completes a full rotation. Motion behavior of elastic members depending on the geometry and loading are investigated using Elastica theory. Kinematic analysis and dynamical model are obtained by representing the compliant pinned-pinned members as translational springs using polynomial formulation method. Mechanism behavior is also analyzed in Adams FlexView. Mechanism is built by 3D printing the flexible parts using polylactic acid (PLA). Displacement of the slider along with the deformation of buckling beams are recorded and deflection shapes are detected by machine vision measurement while the crank is subjected to complete rotation. Slider position is also recorded by a laser displacement sensor. Dynamical model results are validated by the experimental setup, machine vision measurement and Adams simulations.

This study presents the design and development of a compliant multi-link hopping mechanism actuated by a single DC motor. Two main design goals are to have a single piece designed main body for the jumping robot and a passive stabilizer to allow consecutive jumps. Mechanism consists of monolithically designed large deflecting main body incorporating the gears and initially curved flexure hinge. Due to the limitations of the design goal, revolute motion between top and bottom legs on the main body are realized by a compliant link which replaces the need of ball bearings. Also, continuous energy store and release during jumping is ensured by the same flexure hinges. Passive self-righting cage is attached to the bottom of the main body to maintain upright position both in landing and takeoff. The cage allows the center of mass to stay in the vertical plane to prevent tilting. During landing, cage absorbs the impact and allows the main body to roll to its initial configuration so that the robot can complete jumping. Mechanism parts including the cage are 3D printed using PETG. Design optimization of the body parts including the rigid legs and flexure hinges are analyzed both experimentally and analytically. Finite element analysis is performed to calculate the equivalent stiffness and natural frequency of the jumping robot and simplified mathematical model is derived using rigid body dynamics.

Mechanical engineering students often learn the fundamentals of vibrations along with the time response of underdamped, critically damped, and overdamped systems in machine dynamics and vibrations courses without any validation or visualization through hands-on experimental learning activities. As these courses are highly theoretical, students find it difficult to connect theory to practical fundamentals such as modeling of a mechanical system, finding components of the system using experimental data, designing a system to achieve a desired response, or designing a passive vibration isolator to reduce transmitted vibrations on a primary system. Further, available educational laboratory equipment demonstrating vibrations, dynamics and control is expensive, bulky, and not portable. To address these issues, we developed a low-cost, 3D printed, portable laboratory equipment (3D-PLE) system consisting of primary and secondary carts, rail, linear actuator, Arduino, and compliant flexures connecting the carts. Most of the educational systems consist of a mass limited to 1DOF motion and multi-degrees of freedom systems can be created using mechanical springs. However, in real-world applications oscillations in a system are not necessarily due to mechanical springs. Anything flexible, or thin and long, can be represented by a spring as seen in torsional systems. We incorporated 3D printed and two monolithically designed rigid arms connected with a flexure hinge of various stiffness. The carts are designed in a way such that two flexible links can be attached from both sides and allow more loads to be added on each cart. The system can be utilized to demonstrate fundamentals of vibrations and test designs of passive isolators to dampen the oscillations of the primary cart.

This paper presents the informative process of modeling of compliant mechanisms using MATLAB Simscape. Simscape is the modeling environment analyzing both rigid and flexible systems using either the blocks provided in the library or the CAD models imported from modeling software. We present the modeling of four compliant mechanisms: dwell, five bar, translational and hopping mechanisms. Once the cad model of a system is imported into Simscape, the flexible links or flexure segment on each example system is replaced by its equivalent lumped parameter block. Compliant dwell mechanism is comprised of a rail, two pinned-pinned flexible links, slider, rigid crank and a DC motor. The second mechanism is a fully compliant five bar mechanism incorporating large deflecting flexures and actuated by two servo motors. The objective is to control the trajectory of the tip position. Third example models a bio-inspired translational compliant mechanism driven by servo motors and comprised of three sliders connected by single piece designed 2 rigid arm-flexure hinge linkages mimicking the motion of a caterpillar. The last example is the modeling of a compliant hopping robot consisting of two pairs of gears; one pair is attached to the motor and the other pair allows the bottom links to rotate at same angular velocity in opposite directions.

This paper reports on design, fabrication, and kinematics modeling of a 3D printed soft parallel robot equipped with soft pneumatic actuators. Soft robotics is an emerging field of research which facilitates safe human machine interface. Soft elastomeric actuators made through molding process are one of the key elements of soft robotic systems. However, molding process is tedious and time consuming making the fabrication process undesirable. Recently reported 3D printed soft pneumatic actuators pave the way for manufacturing of novel soft actuators and robots with complex geometries. The current work can be considered as a proof of concept for 3D printing of a soft parallel robot. The robot consists of two soft pneumatic actuators that are connected to two passive links by mean of flexible hinges. The robot has two degrees of freedom and can be used in planar manipulation tasks. Moreover, a number of robots can be configured to operate in a cooperative manner to increase the manipulation dexterity. A kinematic model is developed to simulate the motion of robot end-effector. Through application of the kinematic model it has been shown that the robot is capable of following any planar trajectories within its workspace. Also, pseudo-rigid-body model (PRBM) is used to develop a dynamic model of the soft robot to more accurately predict the robot interaction with its environment and also develop advanced control system for robust position control of the robot.

This paper presents the design and development of a two fingered, monolithically designed compliant gripper mounted on a two-link robot. Rigid grippers traditionally designed by rigid links and joints might have low precision due to friction and backlash. The proposed gripper is designed as a single piece compliant mechanism consisted of several flexible links and actuated by wire through a servo motor. The gripper is attached to a two-link arm robot driven by three step motors. An additional servo motor can also rotate the base of the robot. While the robot is 3D printed using polylactic acid (PLA), the gripper is 3D printed in thermoplasticpolyurethane (TPU). Two force sensors are attached to the right and left ends of the gripper to measure grasping force. Experimental testing for grasping various objects having different sizes, shapes and weights is carried out to verify the robust performance of the proposed design. Through the experimentation, it’s been noted that the compliant gripper can successfully lift up objects at a maximum mass of 200 g and have a better performance if the objects’width is closer to the width of the gripper. The presented mechanism can be utilized as a service robot for elderly people to assist them pick and place objects or lift objects if equipped with necessary sensors.

Design and control of human-like robots mimicking the motion using biped legs are still in demand. However, the vast majority of the biped robots are too heavy due to the number of actuators and their bulky design. Compliant designs can mimic the motions in nature through the large deformation of their compliant members and have the ability to be designed as a single piece thereby reducing the overall weight and increasing the performance of the mechanism. Biped robots specifically designed for walking currently existing in the literature often arranged in series form. Although serial design leads high flexibility, each link carries its actuator compromising the overall weight and stability. This paper presents the design and development of a bioinspired leg for biped robots without the requirement of actuation of the knee or addition of a spring element. Each leg is designed as a single piece by exploiting a compliant knee joint, 3D printed using TPU filament and actuated through a cam design using a servo motor. Servo motor is also attached to the trunk which serves as the torso of the robot body. Zero moment point (ZMP) analysis is performed by adopting simple cart-table and inverted pendulum methods. Stiffness of the compliant knee is obtained from multibody dynamic simulations in MSC Adams. The preliminary testing of the bio-inspired biped robot reveals that the robot performs successful periodic gait.

This study presents the design and development of a novel, low-cost load-deflection test setup providing the testing of flexible links and compliant mechanisms. Test bench consists of two stepper motors, lead screw, rail system, two carts, two clamps, bearings and a force sensor. Clamps are designed in a way to attach various types of compliant members such as pinned-pinned buckling beam, fixed-fixed beam and 3D printed links. Mechanism enables to calculate the stiffness of compliant and 3D printed flexible systems. Sliders are displaced quasi-statically to slowly stretch or compress the flexible members attached in between two clamps. Displacement of the carts and deflection of the midpoint of the buckling beams are captured using machine vision measurement. Force applied from one of the carts to the end of the attached link is recorded using the force sensor. Stiffness of 3D printed flexible translational vibratory mechanisms is obtained using the displacement of the carts and load deflection curve of buckling beams are obtained using deflection curve and load data. Experimental results are compared with the same simulations performed by FEA analysis.

There is still a demand for novel laboratory equipment designs that are to be utilized in undergraduate level machine dynamics, mechanical vibrations, control theory and their related labs. Since the turn-key systems preferred in most undergraduate labs are expensive and require wide lab space, 3D printed portable, small scale and cost-effective vibrational lab equipment are designed to study the fundamentals of free and forced vibrations. Four laboratory equipment designs are proposed in this study to demonstrate the fundamentals of vibration such as free vibration, forced vibration, modeling, base excitation and vibration isolation. The first device is a vibration isolator and resonator mechanism incorporating large deflecting fixed-free flexible links and composed of primary and secondary masses and a linear actuator, the second mechanism is a compliant parallel arm consisted of flexible beams, mass and a support, third mechanism is a translational vibratory mechanism comprised of slider carts, 3D printed springs, rods and bearings and the final mechanism is the model of driver seat consisted of DC motor, driver and driven wheels and a mass. Main parts of each apparatus are built by 3D printing using either PLA or PETG filament. Learning outcomes and the methods of implementing each device to the course and their associated laboratories are provided.

This paper investigates the construction, instrumentation, and dynamical modeling of a coupled three degrees of freedom compliant parallel arm mechanism. The compliant parallel arm, whose complete construction is carried out using 3D printing of polylactide (PLA) filaments, is a folded beam type mechanism, which is comprised of one primary and two secondary masses connected to two large deflecting beams. Dynamical model of the complete mechanism is obtained using Elastica Theory, where the large deflecting beams are considered as fixed-free cantilever beams subjected to a vertical tip load. Nonlinear load deflection curve, which is derived from the solutions of elliptical integrals, is approximated by a high-order polynomial function. Finally, the dynamics of the complete mechanism is derived using a classical lumped mass-spring-damper second order system. A linear actuator, PCB triaxial accelerometers, two laser displacement sensors and Arduino are utilized to gather acceleration and position information of each mass to identify the parameters of the lumped second order model using the offline Elastica Theory-based approach and polynomial fitting method. Numerical and experimental results verify the effectiveness of the proposed parameter identification schemes. Since system is nonlinear, state feedback linearization approach is adapted to linearize system equations at all operating points to control the trajectory of primary mass using a PID controller.

This paper investigates design, modeling and fabrication of a flexible five bar mechanism, which incorporates large deflecting flexure hinges attached to rigid links. This 3D printed flexible robotic mechanism is actuated by two servo motors and machine vision is used to obtain its tip position information. Detection of parts accomplished using color thresholding of a dynamic region of interest, while the position of detected elements is measured using the pinhole camera model. Under the assumption of non-small length flexures, where low aspect ratio is not satisfied, we adopt an initially curved pseudo rigid body approach to model each flexure as two rigid links that are pinned on top of each other using torsional springs, which capture the load-deflection behavior of the compliant flexures. Kinematic and dynamical equations are derived using both vector closure loop equations and Euler’s Laws of Motion. Adams simulation is performed by exporting the CAD model as a parasolid file, defining revolute joints and input motions and converting the rigid body to flexible. Mathematical model is validated using both the experimental data and Adams simulations.

This paper presents the design phases and modeling of multi axial compliant prosthetic knee joint comprised of rigid and flexible members providing a better performance than traditional spring-loaded rigid multilink joints. Mechanism consists of monolithic compliant five bar incorporating large deflecting flexure hinges, two rigid body representing the upper and lower legs, translational spring and flexure joints simulating ankle motion. Dynamical modeling is studied by integrating pseudo rigid body modeling of small-length flexure hinge method and Lagrange equations under the assumption that link 2 (left base link) is fixed and link 3 is rotated quasi-statically at constant speed. Torsional stiffness of ankle springs is obtained by using MSC Adams simulations. Initial prototype is built by 3D printing the parts using polylactic acid (PLA) filament. Mechanism is potentially suitable for pediatric prosthetic knee systems due to its simple design, versatility and light weight.

This study presents the design analysis and development of a novel partially compliant bistable mechanism. Motion behavior dependence on links and relative angles are analyzed, lumped parameter model is derived, mechanism parts including the compliant members are three-dimensional (3D) printed and a state feedback controller is implemented so that the slider follows a well-defined trajectory if designed as an actuator. The proposed mechanism consists of initially straight, large deflecting fixed-pinned compliant links, rigid links, and a sliding mass. Dynamic response of the mechanism is studied using elliptic integral solutions, pseudo rigid body model (PRBM), vector closure loop equations and Elliptic integrals. Nonlinear model is simulated in matlab simulink using fourth‐order Runge‐Kutta algorithms. The research emphasizes on the realization and dynamic response of the mechanism and the trajectory control of the slider so that the slider can be kept constant at specified distances resulting a dwell motion if designed as a linear actuator.

Supplemental material, IJJ887140 Supplementary material for Demonstration of vibration control using a compliant parallel arm mechanism by Ayse Tekes, Tris Utschig and Tyler Johns in International Journal of Mechanical Engineering Education

Very little is known about the fracture behaviors of novel nanomaterials such as carbon nanotubes and graphene due to the difficulty of sample manipulation and in situ detection of their failure mechanism. In the present study, the design and analysis of a Microelectromechanical System (MEMs) device is presented for the tensile testing of single layer graphene. The electrostatically actuated dual parallel plate actuators in the proposed MEMS device enable in situ measurement in a scanning electron microscope by stretching the two ends of a nanostructured sample simultaneously. The elongation in the specimen is obtained by nonlinear finite element analysis using COMSOL, and MATLAB. For the validation of the proposed MEMS device, a lumped model of the system is utilized to analyze the stress-strain behavior of the nanostructured sample under the force generated by the electrodes.

Take home lab equipment and hands-on learning tools are still in demand for control theory and vibrations courses. The existing equipment are extremely expensive and require wide lab space. The aim of this research is to build vibratory mechanical system that is compact, modular and small scale so that each student can work on their setup and take it home if necessary. For this purpose, in this study, a semi-compliant mechanism is designed to be utilized in systems control and vibrations courses which would enhance the understanding of students by using experimental demonstration of the theoretical systems. The superiorities of the design over commercially available equipment are their low cost and simplicity. A parallel arm mechanism consisting of several flexible links that can be attached at different points on the slider is designed, finite element analysis (FEA) is performed in Solidworks, and the flexible beams are 3D printed using polyactic acid (PLA) and Polyethylene terephthalate glycol-modified (PETG) filaments. Different configurations of the mechanism are explored by changing the number of flexible beams attached to the slider. The mathematical model of the proposed mechanism can be represented by a single mass and multiple springs in parallel. Since mass is a known property, the equivalent stiffness can be experimentally found from the frequency analysis of free response. For this purpose, a PCB model tri-axial accelerometer is attached to the slider and the equations of motion are derived from the analysis of frequency characteristics of the complaint dual arm mechanism for each configuration. System properties including the equivalent friction are obtained from the acceleration vs time data using logarithmic decrement. The forced response is studied by attaching a load to the mass through a pulley system. The load deflection curve is obtained experimentally from LabVIEW. Since the system parameters are obtained from the free response, Matlab Simulink model outputs for the same initial displacement and force input are verified with the experimental data.

Two adjustable compliant mechanism load deflection test benches are presented in this study. Both test bench mechanisms enable testing the deflection of flexible links or mechanisms. The modularity of the designs provides to test various link forms such as fixed-fixed and pinned-pinned joints. The load deflection test benches consist of a linear actuator, an amplifier rod, a linear rail and a sliding car. The measurement setup is equipped with force and displacement sensors for the linear actuator, various clamps to attach the compliant member, and machine vision software to measure member deflection. A displacement-controlled loading using a linear actuator, rack-pinion attached to a motor, or step loading with a pulley can be applied as an input to the system. There are several limitations involved in the design. First, the length of the test object should be kept between 5 cm to 30 cm. Second, a low cost linear actuator with a low extension velocity to obtain quasi static deflection curves of the compliant members is required. Finally, the design should also have the capability of providing various types of boundary conditions with interchangeable attachments. The force can be applied either parallel or perpendicular to the test object. Input load deflection is measured with the displacement sensor, and the resulting member displacement measured visually using machine vision software. This software synchronizes data from the displacement sensor and a calibrated camera image to automatically detect deflection using a pinhole camera model and known dimensions of the test apparatus. The purpose of this study is to design and fabricate a load deflection test setup capable of testing flexible links and compliant mechanisms. Two different designs are proposed and explored in this study. The first design is the modification of a commercially available ECP Model 210 educational turnkey system favorably utilized in undergraduate level vibrations and control labs. By attaching the designed clamps on two carts, fixed-fixed and U shaped compliant link load deflection can be obtained. Four cases such as fixed-fixed buckling beam, U shaped beam buckling with one end sliding, already buckled beam loaded at its upper midpoint, and inverse U-shaped beam loaded at its apex to form deflected M beam (with design 2) are considered. In order to achieve buckled beam experiments in which the load is applied at the midpoint of the already buckled links, a new test bench consisting of a linear actuator, rigid links, rail and two sliding cars is designed.

In this study, two degrees of freedom planar compliant five-bar mechanism design is explored and synthesized to achieve a desired trajectory and to perform various defined tasks. The mechanism consists of five rigid links (including the ground) connected by the compliant large deflecting short beam joints and it is excited by the applied torques at the base links. The compliant five bar mechanism has not been explored in the literature for either a path tracking task or a function generation problem. The novelty of the compliant five bar mechanism presented in this paper is its large deflecting/rotating pivots joining the mechanism links. The mathematical model of the compliant five-bar mechanism is derived by using vector loop closures and dynamic inertia equations of the mechanism links. The dynamic response of the mechanism is investigated under the applied torques to the corresponding base links, using numerical 4th order Runge-Kutta methods. Compliant joints are represented by their equivalent torsional spring parameters so that the nonlinear large deflection equations of short beam joints are eliminated from the kinematic equations of the system using its equivalent Pseudo Rigid Body Model (PRBM). The torsional spring constants can be obtained, either by using nonlinear exact mathematical equations or by using geometrically nonlinear Finite Element Method software. The scope of this research is to derive a mathematical model of the system and to analyze the compliant five bar mechanism including the controller design for arbitrary predefined tasks to achieve the desired path for the end effector. The compliant five-bar mechanisms are superior to traditional rigid five-bar mechanisms in high precision tasks since compliant joints and links have no backlash and friction. This study explores path generation of compliant five bar mechanism resulting in high precision path tracking. The presented mechanism might be manufactured as a single piece using an injection molding technique or 3D printing by polypropylene and it is also suitable for a fully compliant Micro Electro Mechanical System fabrication. The mathematical model of the mechanism is validated by utilizing inverse-forward dynamic model. The tip point of the mechanism successfully follows the reference trajectory by employing model based PID controller.

We employ molecular dynamics simulations to explore the effect of tensile strain on the thermal conductivity of carbon nanotube (CNT)–graphene junction structures. Two types of CNT–graphene junctions are simulated; a seamless junction between CNT and graphene with pure [Formula: see text] covalent bonds, and a junction with mixed [Formula: see text] covalent bonds are studied. The most interesting observation is that the thermal conductivity of a CNT–graphene junction structure increases with an increase in mechanical strain. For the case of a (6,6) CNT–graphene junction structure with an inter-pillar distance (the length of graphene floor between two CNT–graphene junctions) of 15[Formula: see text]nm, the thermal conductivity is improved by 22.4% with 0.1 tensile strain. The thermal conductivity improvement by mechanical strain is enhanced when a larger graphene floor is placed between junctions since a larger graphene floor allows larger deformation (larger tensile strain) without breaking bonds in the junction structure. However, the thermal conductivity is found to more strongly depend on the C–C bond hybridization at the intramolecular junctions with pure [Formula: see text] hybridization showing a higher thermal conductivity when compared to mixed [Formula: see text] bonding regardless of the amount of tensile strain. The obtained results will contribute to the development of flexible electronics by providing a theoretical background on the thermal transport of three-dimensional carbon nanostructures under deformation.

The control of a slider-crank mechanism driven by a compliant, folded beam mechanism is investigated in this study. The compliant folded beam mechanism, also called the compliant double arm mechanism, has application areas at both the micro and macro levels. The compliant folded beam mechanism control in micro dimensions, driven by a force actuator is investigated here. The kinematic synthesis of the mechanism has been studied using mathematically exact nonlinear Elastica theory. The equivalent stiffness of the large deflecting fixed-free flexible beam, the single arm beam and the complete folded beam mechanism (double arm mechanism) are computed and, the complete mechanism stiffness is represented by a polynomial function that is curve fitted to the nonlinear inextensible exact beam theory solution. The dynamic response of the mechanism is obtained by solving the nonlinear equation of motion numerically using Runge-Kutta methods. The emphasis of the paper is placed on the subject of control of compliant mechanisms incorporating nonlinear stiffness (having large deflections) for function generation. The trajectory control of double cranks is achieved by considering linearization by the state feedback since the compliant folded beam mechanism (the double parallel arm mechanism) has a nonlinear stiffness. A PD controller is then applied to the feedback linearized system. The controller coefficients are determined to satisfy desired specifications on the output of the system. (C) 2010 Elsevier Ltd. All rights reserved.