Individual Report Oli Thompson Abstract Jumping Is an Alternative Means of Locomotion for Small Scale Robots and Offers Various Advantages Over Wheels Or Legs
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Gizmo Individual Report Oli Thompson Abstract Jumping is an alternative means of locomotion for small scale robots and offers various advantages over wheels or legs. The speed and efficacy of traditional robots is significantly constrained by the conditions and terrain of travel. This problem becomes more pronounced with smaller robots who are unable to manoeuvre over objects above certain radii. Jumping robots are affected less by terrain and can traverse much larger obstacles, making them ideal for use in hard to reach areas; a practical example being search and rescue. This report details the development and design of a monopod jumping robot. The engineering challenges associated with jumping robots include weight limitations, self-righting mechanisms, ingress protection, jump height and distance, less accurate control over locomotion and the difficulties of changing direction mid-jump. These are all challenges that work against each other, and each required careful consideration throughout. Following initial sketches research into boimocry of jumping animals and insects, the design process involved calculating the dynamics of the jumping system using matlab to establish the required spec- ification of the important components (e.g. motor and gearbox). Block sketches and initial CAD were iterated upon until a Solidworks 2017 assembly of the final robot was completed. This model was tested with for various failure modes and flow simulation was used to analyse the robot’s propeller and rudder mechanisms. The finished robot’s calculated jump height and distance are aproximately 1m x and 2m respectively. The housing satisfies a minimum IP54 rating and is capable of at least twenty jumps on a single charge. In addition to this the robot can right itself regardless of its landing orientation and is able to change the horizontal locomotion force using a variable pitch propeller which allows precise control over the launch trajectory. The jump speed is also variable allowing the robot to jump to different heights. The robot’s total mass is 195.29g, not including the black box containing the electronics, (the weight of which was not given) and the total cost of the robot came to £82.81; this figure includes the retail price of all standard and purchased components, and the prices of the various raw materials used. Manufacturing costs were not included as the manufacturing volume was not specified; a single prototype would have considerably higher initial costs wheras were it mass produced the cost figure would be more accurate. The blackbox was also not included in this figure as this report details the the mechanical aspects of design, and not the elctronics or control systems. Contents Abstract 2 Abbreviations & Nomenclature 3 Introduction 3 Research 3 Calculations 5 Bought Components 6 Morphological Analysis 7 Initial Sketches 7 Manufacture 7 Iterative Design 8 Mechanisms 9 Key Components 13 Flow Simulation 15 Conclusion 16 References 17 2 Abbreviations & Nomenclature CoM – Centre of mass I - Current LiPo – Lithium Polymer V - Voltage FEA - Finite Element Analysis a - Acceleration m – Mass NA – Number of turns IP – Ingress Protection h – Hours ABS - Acrylonitrile Butadiene Styrene µ - Coefficient of friction CD – Coefficient of Drag G – Shear Modulus t – Time k - Spring rate J - Joules S - Displacement g – Gravitational force at sea level ρ - Angular Velocity ρ – Density n - Factor of Safety E – Energy Ct - Shock Fatigue Factor, Torques Fy – Force acting vertically Cm - Shock Fatigue Factor, Moments Fx – Force acting horizontally Sy - Tensile Yield Strength Fair – Opposing Force from air resistance T - Shaft Torque P – Power M - Applied Bending Moment v – Velocity Ft - Tangential Component of Tooth Force r – Radius Kv - Velocity Factor d – Wire Diameter V- Pitch Line Velocity D - Diameter ba - Face Width v0 – Initial Velocity Y - Lewis Number rpm – Revolutions per Minute m - Module ρ – Torque ρ - Bending Stress Introduction Jumping robots offer greater agility in rough terrain than typical Criteria Value robots and design inspiration can be drawn from the various Jump Height 300 mm jumping animals and insects found in nature. The monopod robot had to be designed to meet the technical metrics in table 1. The Jump Distance 300 mm electronics and control aspects of this robot will not be detailed Cost < £100 in this report and are represented by a black box of dimensions Mass < 200g 10mm x 20mm x 45mm which was housed within the robot in accordance with the ingress protection criteria. An optional Ingress Protection IP54 challenge was to control the angles of trajectory and yaw during Table 1 the jump. Research Biomimicry proves particularly useful when designing linkages that transfer the largest force from the muscle (or spring) to the ground with maximum efficiency. It is equally important that the thrust force acts over a short period of time otherwise the leg will have reached full extension before the force reaches its maximum. Both animals and insects can exhibit impressive jumping abilities. The biology of animals is considerably more complex than that of insects; when looking at leg joints animals typically have more degrees of freedom allowing greater articulation and asymmetric movement over their two hind legs. When adapting a bipedal jumping mechanism into a single foot this complexity of motion introduces several unknowns. Muscle contraction is the typical source of energy in a jumping mammal, with elastic mechanisms (usually tendons) saving 20% - 30% of the metabolic energy required for saltation. Insects rely predominantly on the elasticity of a cuticle made from resillin, a material that demonstrates near perfect elasticity with 97% of the stored energy being released as mechanical energy. As a result, the jumping mechanism for an insect is more analogous to a sprung linkage operating in a single plane than that of a mammal and as such insects rather than mammals were chosen as a basis for research. The flea is able to attain the highest jump height of any insect in relation to its size, followed by the froghopper and grasshopper. When borrowing effective design from nature it is necessary to consider the effects of scale; most insects have a much smaller surface area to volume ratio than robots of this size, and it is not guaranteed that the mathematics of motion will still give the desired results because of the square cube law. With this in mind the jumping mechanism of the grasshopper was chosen for further research and development as they are typically 30 and 20 times larger than the flea and froghopper respectively (grasshoppers typically measure 50mm in length), 2 even if the relative jump height is less. 3 During a jump a grasshopper stores around 50% of the energy in the femur-tibia joint, with the remainder stored in the extensor tendon and the cuticle of the femur (Figure 1). The grasshopper begins by inducing flexion in the femur tibia joint, and angling the coxa femur joint to control launch elevation. It is worth noting that the grasshopper can release the sprung joint regardless of how much energy is stored; allowing precise control over launch velocity. The tibia tarsus joint Figure 1 - Grasshopper hind leg plays no role in the jumping mechanism and serves to improve traction with the ground during the jump. The coxa-femur, femur-tibia and tibia tarsus joints all have a single degree of freedom and are as such well suited to a two dimensional linkage system. The experimental data shown in Table 2, along with the plot of angular position against time (Figure 2) can be used to design a linkage mechanism as close as possible to that of the grasshopper. The dimensions were scaled up and equation driven Solidworks sketches were used as a basis for the iterative design process of the linkage (Figure 3), as a precursor to 3D modelling. By examining the angles between tibia and femur it became apparent that the linkage had to move Figure 2 - Joint angles throughout jump - http://citeseerx.ist.psu.edu/ symmetrically, with the thorax - knee joint viewdoc/download?doi=10.1.1.98.4074&rep=rep1&type=pdf distance roughly equal to the tarsus knee Total body mass (M) 415 mg joint distance at all times during the jump. This critical geometry enables the linkage Tibia length 15.6 mm to maintain a linear direction of force Femur length 17.1mm which is essential for maximum efficiency. Body Linkage Design Structure Femur max - min diameter 3.2 - 0.8 mm Firstly consideration was given to the Tibia tubular diameter 0.6 mm linkage design as the calculations overleaf rely on the linkage geometry. A Angle of rotation of tibia 165 ° grasshopper is able to control 3 joints to Horizontal distance 302 mm ensure linearity, but to use this method in Jumping a robot would require 3 extra actuators. Performance Take-off angle 33.8 ° Instead a parallel linkage can be used Potential Energy 20 µJ to keep the chassis in line with the ground, but this method fails to control the Table 2 - http://citeseerx.ist.psu.edu/viewdoc/download?- geometric symmetry. This was solved with doi=10.1.1.98.4074&rep=rep1&type=pdf the final linkage iteration which utilised gear segments at a 1:1 ratio attached to opposite linkages to ensure even expansion and contraction of the leg (Figure 4). These gears included hollow sections in order to reduce weight. Figure 3 - Grasshopper Linkage sketch Figure 4 - Geared linkage 4 The grasshopper relies on the grip in its tarsus to push itself into a forward launch trajectory rather than a vertical one, by contrast the robot only relies on the propeller for its forwards motion and only requires the linkage to gain height. A grasshopper’s launch angle is variable, but achieves maximum distance at 33.8° ±10.2°; degrees, this means that the mechanism must be rotated through this Reinforcing Boss same angle to give the maximum vertical launch velocity.