Articulation between body segments of small insects and animals is a three degree-of-freedom (DOF) motion. Implementing this kind of motion in a compact robot is usually not tractable due to limitations in small actuator technologies. In this work, we concede full 3-DOF control and instead select a one degree-of-freedom curve in SO(3) to articulate segments of a caterpillar robot. The curve is approximated with a spherical four-bar, which is synthesized through optimal rigid body guidance. We specify the desired SO(3) motion using discrete task positions, then solve for candidate mechanisms by computing all roots of the stationary conditions using numerical homotopy continuation. A caterpillar robot prototype demonstrates the utility of this approach. This synthesis procedure is also used to design prolegs for the caterpillar robot. Each segment contains two DC motors and a shape memory alloy, which is used for latching and unlatching between segments. The caterpillar robot is capable of walking, steering, object manipulation, body articulation, and climbing.

There are many ways for a gripper to estimate the forces between its fingers. If powered by direct-drive brushless motors, then one technique is to measure their current. This is not the most accurate technique, but it is simple, keeps the sensor remote, and requires no new components. The estimation involves multiplying current signals through by the torque constant and the inverse transpose of the Jacobian. The Jacobian either amplifies the signal from fingertip force to motor current (at the cost of tip force production), or diminishes it (with the gain of tip force production), indicating an inherent trade-off. However, the Jacobian is a function of configuration, and for any workspace point there are multiple configurations (multiple inverse kinematics solutions), therefore a selection of Jacobian exists. For a given workspace point, the number of Jacobian choices is just a few, but these choices can be designed (through dimensional synthesis) to overcome the trade-off. The problem can be framed as velocity ellipse synthesis over multiple output modes. In this work, we conduct optimal synthesis to compute a new gripper design. The gripper was built and tested. It transitions between two different modes: sense mode and grip mode. Sense mode can sense forces 3 times smaller than grip mode. Grip mode can exert forces 4 times greater than sense mode.

The configuration spaces of parallel manipulators exhibit more nonlinearity than serial manipulators. Qualitatively, they can be seen to possess extra folds. Projection onto smaller spaces of engineering relevance, such as an output workspace or an input actuator space, these folds cast edges that exhibit boundary behavior. For example, inside the global workspace bounds of a five-bar linkage appear several local workspace bounds that only constrain certain output modes of the mechanism. The presence of such boundaries, which manifest in both input and output projections, serve as a source of confusion when these projections are studied exclusively instead of the configuration space itself. Particularly, the design of nonsymmetric parallel manipulators has been confounded by the presence of exotic projections in their input and output spaces. In this paper, we represent the configuration space with a radius graph, then weight each edge by solving an optimization problem using homotopy continuation to quantify transmission quality. We then employ a graph path planner to approximate geodesics between configuration points that avoid regions of low transmission quality. Our methodology automatically generates paths capable of transitioning between non-neighboring output modes, a motion which involves osculating multiple workspace boundaries (local, global, or both). We apply our technique to two nonsymmetric five-bar examples that demonstrate how transmission properties and other characteristics of the workspace can be selected by switching output modes.

This paper reports on preliminary experimental results of recently proposed mechanism kinematics for a legged robot. The proposed kinematics creates a mapping from a series-elastic actuator to a foot motion that includes a pair of singularities within a fully rotatable kinematic circuit. Such a circuit is less common and only possible with certain multi-loop linkages. A slice of the configuration space displaying series-elastic rotation versus linear foot motion presents a characteristic “S” shape, motivating the name S-curve kinematics. Our experimental results show that S-curve kinematics can enhance the energetic output of a series-elastic actuator in a hopping task versus the usage of a conventional rotary-to-linear mechanism. This is possible because S-curve kinematics enable elastic energy storage outside of stance that is released through a mechanical reflex. Compared to a conventional rotary-to-linear actuator, S-curve kinematics demonstrated up to a 4x increase in kinetic output.

Kinematics is the first consideration in designing the mechanical structures that comprise robots. Of the many subcategories that exist under this umbrella, an often early design goal is to achieve some desired workspace. This goal applies to both single and multi-degree-of-freedom systems. Previous literature has applied the diversity of extant optimization techniques for achieving such design goals. A conceptually simple approach to single-objective optimization is to symbolically derive a gradient vector, then find all of its zeroes. This approach is easier said than done since the resulting system is nonlinear. For this reason, sophisticated optimization heuristics are more commonly employed. In this paper, we revitalize the former approach, offering a route to efficiently find all of the gradient zeroes, including the global minimum. Our approach is facilitated by homotopy continuation. We connect the theoretical results to practical problems by demonstrating the design of a mechanism for a humanoid walking gait and the finger of a robotic hand.

Polar linkages have two degrees-of-freedom (DOF) where one input joint angle controls the length of a radial segment while another controls its angle. Considering a theoretical planar robot model, this mapping between joint angles to output motions can be shown to be energetically advantageous over the ubiquitous two-revolute linkage. Since a polar linkage’s typical construction involves a moving prismatic joint, it is cumbersome to implement alongside rotary electromagnetic actuators offsetting any advantage. In this paper, we present a procedure for designing polar linkages using only revolute joints. The procedure starts with a pre-existing single DOF straight line linkage and then finds the dimensions of a three-link attachment to produce the second DOF. In the end, the straight line linkage actuates the polar length and the attachment actuates the polar angle. The design process is framed under optimization with an objective that is both polynomial and invariant to the number of discretization points. This enables the techniques of numerical continuation to efficiently find complete sets of minima. We demonstrate our procedure with an example in which multiple minima are found including the global minimum. This computed design solution is then fabricated in order to validate the designed kinematics.

Legged robots primarily energize their center of mass through external contact during stance phase. This links their range of possible motions to actuator power limits applied during usually short periods of time. Enabling limb actuators to pump energy into the system during non-contact phases can greatly extend the energetic profile of possible motions. However, funneling this extra energy into useful dynamics is a problem of its own. In this paper, we propose designing limb mechanisms that purposefully integrate kinematic singularities into their configuration space to enable airborne energization and enhance gait periodicity before sensors and feedback control are incorporated. The result produces a mechanical reflex that unloads spring energy stored during flight phase into a useful push-off motion as triggered by the onset of stance phase. The implementation generates an "S" shaped curve into a specific slice of the configuration space, motivating the name S-curve. We compare our proposed approach to more conventional strategies and survey the design parameters that can be used to shape an S-curve. Ranges of useful S-curves are determined through a simulation study and a linkage mechanism capable of producing an S-curve is displayed.

Achieving high-performance dynamic behavior in a robot requires careful design of morphology. However, searching for a global optimum morphology in an intensely nonlinear design space is difficult, especially if stochastic seeding is used. In contrast to optimization, we encode design requirements into a polynomial system with a huge number of isolated roots. Each root describes an alternate robot morphology in the design space. Following this, the computation of nearly all isolated roots constitutes design space exploration. Previously, these systems were intractable, due to the heavy burden of degenerate roots. We relieve this burden by using the finite root generation (FRG) method to enable the discovery of nearly all isolated roots for a certain six-bar design problem for the first time. The FRG synthesis method enables the design of a transmission function from motor dynamics to a loaded end effector to influence the overall dynamic behavior. In an example, we formulate synthesis equations which were previously intractable, obtain 1 528 608 isolated roots (estimated 99.0%), and find 3764 physical designs. Design options are compared according to their sensitivity to joint errors.

Recent work in the design of mechanical systems for terrestrial locomotion has indicated successful strategies for increasing the energetic performance of a robotic locomotor without upgrading its actuator system. We apply one such strategy, termed power modulation, in a new way: for the design of a leg mechanism useful for running. Power modulation geometrically defines force/torque ratios between robot components to mechanically achieve certain energy transmission characteristics during fast stance dynamics that increase the kinetic power output of the overall system. Furthermore, we investigate the design of a leg mechanism that can adjust to exhibit power modulation. In this way, a leg mechanism would exhibit a low power mode for flat terrain, and can adjust to a high power mode for rough terrain. The latter makes jumping possible and extends the range of available footholds that can be accessed in a single step. To find a suitable leg mechanism, we leverage the Finite Root Generation method to compute a design. The design is advanced to a prototype and basic experiments are conducted to investigate its behavior as adjusted between high-and low-power modes.

Due to high impact forces and low duty cycles, monopedal jumping robots are particularly susceptible to failure from a slipping foot. Spines provide a solution to reduce slip, but there has been little research on how to effectively engage them into a surface with a dynamic jumping robot. Previous robots utilizing spines operate in different regimes of surface approach speed and cycle time. For a penetrable substrate, spines must be directed into the surface at suitable holding angles, then extracted before the foot leaves the ground. We accomplished this by designing a gripper mechanism for the robot Salto that pushes in angled spines along their length and is kinematically constrained to engage/disengage with leg crouch/extension. The resulting mechanism introduces no new actuators, enables jumping on penetrable inclines up to 60°, and enables static adhesion to hold 7.5 times the robot's weight from a ceiling.

Automatic folding has drawn increasing attention in robotics research in the past ten years. The focus has been on folding two-dimensional (2D) sheets into three-dimensional (3D) structures, but little work has been done on how structures may be formed by folding ribbons. Here we propose the concept of robotic ribbon folding including a general workflow from shape design to ribbon folding and shape retention. We also propose a method to realize robotic ribbon folding on the macroscopic scale. The method consists of minimally engineered ribbons with patterned flexures, a folding robot, and a folding scheme that relates the orientation of flexures, the type of folds and the type of structural elements. By using this method we demonstrate robotic ribbon folding into 2D static structures such as triangles and squares, 3D static structures, and planar kinematic linkages such as a simple non-crossing four-bar mechanism. Burn-in result shows a four-bar mechanism with all bars' length of 5 cm could move for over 660 cycles.

New work in robotics targets the development of controllable agile motions such as leaping. In this work, we examine animal and robotic systems on the metric of jumping agility and find that animals can outperform the most agile robots by a factor of two. These specially adapted animals use a jumping strategy we term power modulation to generate more peak power for jumping than otherwise possible. A novel eight-bar revolute mechanism designed with a new linkage synthesis approach encodes the properties for power modulation as well as constraints which assure rotation-free jumping motion. We fabricate an 85 gram prototype and demonstrate that it can perform a range of jumps while constrained by a linear slide. The prototype can deliver 3.63 times more peak jumping power than the maximum its motor can produce. A simulation matched to the physical parameters of the prototype predicts that the robot can attain an agility exceeding that of the most agile animals if the actuator power is increased to 15W.