The Problem

Sheet materials are being used increasingly often in the construction industry. Plasterboard (or drywall) is the most commonly used example. These materials are generally not excessively heavy; the sheet of plasterboard above would have a mass of approximately 20kg. This is below the expected carrying capacity for construction workers but enough that manually gripping the sheet solely from one edge is unviable. Instead of their mass, the challenge of manually handling these sheet materials stems from their unwieldy dimensions. A variety of methods are currently used: carrying with the long side vertical, carrying with multiple people, or carrying flat overhead. These methods are either inefficient or present avoidable safety hazards.

In order to better transport these sheet materials, a gripping device can be used to lift the board from its top edge. This also removes the need to bend over to lift sheet materials, lessening long-term lower body strain.

Design Concept

Base Concept

Utilizing Parametric Design

Analytical Model

Constraints and Objectives

For an analytical model to be built, objectives and constraints need to be determined. 

One objective is minimizing the mass of the mechanism, which is dependent on the total length of links as well as their required radii. The required radius for each link is dependent on the stress it must withstand. The other objective is maximizing the Total Force Ratio. This is defined as the grip force the user needs to apply to the handle to lift a certain load, divided by the weight of that load. Since the Total Force Ratio differs depending on the thickness and surface texture of the sheet material being lifted, a weighted average value was calculated across 18 common usage situations. 

Most of the constraints are geometrical: all the links must be straight (with the exception of link 1); all links must be fixed length (with the exception of link 3); the vertical distance between the two pads must not be large enough to cause failure at any point; the links must not collide with other links or pads at any point; the mechanism must allow for the horizontal distance between the pads faces to smoothly vary between 0mm and 50mm (determined by researching competing products and reviewing common usage situations). Further constraints can be found in the full report.

Checking Constraints

The first section of the analytical model examines whether the generated parameters fit the constraints. Trigonometric equations allow for the locations of every link and pad to be calculated for all mechanism positions. Therefore, the grip range of the mechanism can be automatically evaluated. The same equations can be used to see whether any pair of links will collide at any point. Though, In order to check whether the grip pads will collide with links during motion, the lower bound for the grip pads' height needs to be found.

Finite Element Analysis was used for this. Multiple iterations of the assembly below were analysed with varied vertical displacements between the grip pads.

The analysis showed that the proportion of force transferred between the pads through the load material is 80% up to the point where the ratio between the vertical displacement and pad height is equal to 0.4. As the ratio increases beyond 0.4 the proportion of force transferred decreases drastically. This means the minimum pad height is 2.5 times larger than the maximum vertical distance between the pads. Since the maximum vertical distance between the pads can also be calculated trigonometrically, the required pad height can be found for any iteration of the mechanism.

Evaluating the Total Force Ratio

If the mechanism iteration doesn't break any of the currently calculatable constraints, the model begins to evaluate how well it achieves the objectives. First, it calculates the Total Force Ratio (the user-provided gripping force needed to grip a certain load divided by the weight of that load). To do this, the force transfer through the mechanism needs to be understood. There are two modes of force transfer between the grip pads: 

By creating equations to represent each of these modes of force transfer, an iterative model was developed to describe the behaviour of the mechanism as it lifted a load material. The model begins with the initial condition of the load material at rest on the ground, and the user applying no force on the handle. Then, the user-applied force steadily increases and the cyclical force transfer equations iteratively predict the step of the process. This repeats until the user-applied force has reached its theoretical maximum. 

The point where the frictional gripping force between the two pads is larger than the load material's weight is the point where the material can be lifted. The user-supplied grip force at this point is the minimum necessary and is used to calculate the Total Force Ratio.

Since the Total Force Ratio differs depending on the load material's thickness and surface, the model is repeated for multiple lifting scenarios. This is simulated by altering each plate's coefficient of friction with the load material as well as the horizontal and vertical distance between the plates.

Evaluating the Relative Mass

The other objective is minimizing mass. Since the value for mass is only used for comparative purposes, approximations can be made regarding stress behaviour and material properties.

To calculate the minimum mass for each mechanism iteration, the stresses in each link must be known. The forces and moments acting on each link can be found using the above iterative mechanism behaviour model. Then, by approximating each link as a beam, their minimum viable radii can be found.

The pads themselves contribute a significant proportion of the mechanism's mass, so their weight must also be calculated even for comparative purposes. The minimum pad height is already calculatable as described above, so what remains are the lower bounds for the pad width and pad thickness.

The minimum pad width can be found using the constraint that the mechanism must be able to grip sheet material even when the gripping position is displaced horizontally up to 50mm from the sheet's centre of mass. 

The required pad thickness uses a stress-based approach similar to when calculating the minimum link radii. Each pad is modelled as a simply supported rectangular plate with a force applied through a circular area at its centre. Using the forces from the iterative behaviour model and the known stress equation for this situation, the minimum pad thickness can be found. 

With all this information an approximate value for the mass of each mechanism iteration can be automatically calculated. 

Results

While other mechanism iterations appear to perform better than the optimal, those iterations were found through manual inspection to be unviable. In the vast majority of cases, this was due to required link radii large enough relative to the link's length to prevent the mechanism from functioning as modelled. A future addition to the process would be to automatically detect and remove the iterations with this flaw.

For comparative purposes, a mechanism iteration with manually chosen values for each parameter was also generated and modelled. This is shown on the graph in green. It can be seen that the optimal design generative through the parametric design process is a significant improvement on this manually created one; the average grip force required is 24.8% lower and its mass is 12.2% lower. 

Evaluation

Evaluating the success of the project is challenging. The model shows that the optimized version reduces the pure gripping force needed to lift a standard 2400mm by 1200mm by 12.5mm plasterboard sheet by a factor of 6, while the mechanism only has an estimated mass of 8.96kg. Judging from these numbers, the project would be deemed a success. However, as the project was conducted during the Covid-19 pandemic, creating a prototype to validate these figures, or running experiments to validate assumptions made during the modelling process wasn't possible. For example, the finite element analysis regarding the maximum viable vertical displacement between the pads would have to be physically verified. Also ideally, a very rough physical version of the base concept mechanism would be created before the parametric optimization process began in order to ensure the mechanism functions as predicted.

As discussed earlier, the parametric design process yielded significant improvement over the manually created mechanism. These improvements were absolutely worthwhile relative to the increased difficulty and cost of the development process. However, it is likely a better iteration could still be found. Computing power and time limited the number of iterations that could be tested. A rigorous method could be used to generate the values for the parameters, reducing the likelihood of an optimal solution being simply missed. Another stage of optimization using far smaller variations could be carried out on the current optimal design.

The parametric optimization could also be improved by incorporating more constraints and more diligently calculating the objectives. For example, the possibility of fracture failure in the links and pads is not considered in the model and may give a higher upper bound for the mechanism's mass. Constraints such as the maximum link radius could also be implemented. Considerations of forces and friction losses at joints could influence decisions regarding joint design and optimal force transfer.

Another avenue for possible improvement is revisiting and altering the base design. For example, the base mechanism could be changed to alter the relative movement paths of the two pads, minimizing their vertical displacement. Also, fixed parameters such as the position where the links and pads are joined, and the join method and geometry could be incorporated into the parametric optimization process. 

A further possibility is expanding the scope of the project to look at the gripper product as a whole rather than focusing on solely the bare-bones mechanism. The handle ergonomics, the viability of supporting the load material's weight on the user's shoulder, and the ease of affixing the gripper to the load material are a selection of issues that must be addressed before the gripper could be a viable, practical product.

 For access to the full design report, get in touch at Michaelsvanidze0@gmail.com.