Sourav Rakshit

Resonance occurs when the natural frequency of the system matches with the vibrating frequency. It may cause structural instabilities. To avoid this, engineers maximize the first natural frequency of the system. In many applications, the natural frequency is pre-designed. Structural engineers aim to reduce the weight of structures subject to functional and safety constraints. This motivates us to modify the frequency optimization problem to weight minimization problem, for a specified fundamental natural frequency. In this paper, we solve for weight minimization using topology optimization subject to lower bound constraint on fundamental frequency.

The research toward finding optimal material layout (topology optimization) with design-dependent loads has been going on for more than two decades now. In almost all these research works, the material model is assumed to be isotropic. This work presents the method and demonstrates topology optimization with design-dependent loads for an orthotropic material model. Minimization of structural compliance is selected as the objective, with a constraint on the material used. The solid anisotropic material with penalization (SAMP) model relates elastic constants and element density. A simple boundary identification method is proposed in order to find the load curve. Once the load curve is obtained, loads are directly applied to the nodes of the boundary elements. Finally, numerical examples are presented to demonstrate the proposed approach.

The aim of this work is to conceptualize, design and develop a device to assist the sit-to-stand (STS) motion for disabled and elderly. The device assists the human to stand up from sitting position along the natural trajectory of STS motion. Both human and device are assumed to be functioning fully in the sagittal plane. The natural trajectory of armpit is found for the STS motion using a motion capture system. The coordinates are projected onto a sagittal plane passing through the ankle. A four-bar mechanism is synthesized with four-position motion generation using Burmester curve theory. Assuming quasi-static motion, forces on joints at different time steps are found out. Finite element analysis (FEA) is carried out to determine the required cross section of the links of the structural components of device. Material and dimensions of STS device components are selected, and the device is fabricated. Final experiments of STS device with human show that while using the device, the ground reaction force (GRF) of the human during STS motion decreases by approximately 25%, thereby indicating a reduction in effort of the human for STS by the same order.

The current computation models for gear contact analysis and wear prediction are mostly based on finite element analysis which consumes much computation time and effort. In this work, we adopt an alternative approach for gear contact analysis using linear complementarity. This approach was successfully applied to a pair of rigid spur gears and a planetary gear train (gears are considered as rigid bodies) in our previous work. In this paper, we extend our linear complementarity model to consider local deformation caused due to contact between gear teeth in mesh. Thus obtained linear complementarity model is applied to a pair of spur gears and a planetary gear train. A linear complementarity solver computes the contact forces between meshing teeth of gears. From the contact forces, sliding wear in gear teeth is predicted. Archard’s wear model is used for the wear prediction. Using this model, the contact forces are uniquely determined for the examples considered. The results of linear complementarity and finite element model for a pair of spur gears are compared. The linear complementarity model consumes much less computation time than the finite element model.

This paper proposes a novel heuristic for searching a set of surfaces eligible for providing form-closure grasp of robotic fingers on a rigid polyhedral 3-D object. The key idea that drives the search of eligible surfaces is the formal definition of a convex hull which describes convex hull of a set of points as the smallest convex polygon containing all the points of that set. Eligibility determination of a set of surfaces is carried out by the test based on ray-shooting algorithm (Liu IEEE Trans Robot Automat 15(1):163–173, 1999, [1]), which is formalization of the necessary and sufficient condition for form-closure grasps requiring that the origin of the wrench space lies inside the convex hull of the primitive contact wrenches (Algorithm Spec Issue Robot 2(4):541–558, 1987, [2]). The implementation of three numerical examples demonstrates the usefulness and efficiency of the proposed heuristic.

During simultaneous impacts in linkages connected by joints, there can be several sequences of pair-wise impulse propagation and the choice of the most accurate sequence involves a combinatorial evaluation of all possible impulse sequences.In this paper, a simultaneous impact algorithm for planar frictionless constrained multibody systems is proposed that does not require an impulse propagation sequence to be determined.The formulation is developed by extending the generalized Newtonian restitution model for simultaneous impacts in unconstrained rigid bodies presented in [1] to planar linkages connected by frictionless joints.The algorithm is a computationally efficient alternative to the modeling of collisions in force-based continuous-time domains [2, 3], never results in an increase in kinetic energy (K.E.) [1] and predicts contact separation between bodies having zero pre-impact relative velocity of approach.Results using the proposed algorithm showing various collision scenarios in constrained linkages are included in the paper.Furthermore, the solutions are compared with linear complementarity (LCP) [4]-based approach and simulation results from ADAMS software.

We present a trajectory optimization formulation for the design of a sit-to-stand assistive device for humans with motion impairments. We develop a constrained Lagrangian to derive the equations of motion for the trajectory optimization formulation. Such a Lagrangian enables us to impose constraints on joint reaction wrenches in the human, to simulate the motion impairment of human joints due to injury and infirmity. Using trajectory optimization, we compute the optimal sit-to-stand motions of a human as well as the actuation wrenches of the sit-to-stand device. The trajectory of the device as it follows and supports the human, and its actuation wrenches provide necessary inputs for the design of the assistive device. We propose an assistive device capable of following the natural trajectory of the human during sit-to-stand. We show by numerical simulation that the human requires less effort with the device that can follow its trajectory than with an assistive device restricted to only vertical motion to lift up a human. Our formulation provides a systematic approach for the design of such sit-to-stand assistive devices.

Pelvic bone is a complex and robust load-bearing skeletal structure in the human body, the evolution of which might have been influenced by mechanical loads of daily activities like walking, upright standing, and running. Since the main function of skeletal bones is to provide rigidity to the body and provide hard surfaces for muscle attachment as well, in this work we propose a compliance minimization problem to determine whether material distribution guided by topology optimization yields a skeletal structure similar to the pelvic bone under same boundary conditions and volumetric constraints. As bone growth occurs in response to the mechanical loads acting on it, we consider the maximal loads that the pelvic bone may experience for a continued period of time, namely during running. The running gait cycle is divided into seven phases, and the objective function is a weighted combination of these seven phases. The optimal geometries are compared with the natural hemi-pelvis by measuring shape similarity using Procrustes analysis. Results show that the optimal geometries have good shape similarity in stance phases. We also explore the design space by considering a combination of sequence of phases which is an alternative to the weighted multiple load-case objective function. In all cases, the optimal geometries are stiffer than the hip bone. To validate this result, we conducted compression test experiments on selected optimal geometries and natural hemi-pelvis model of same material and found that the experimental results prove that topology optimization based optimal geometries are indeed more stiff than the natural hemi-pelvis geometry.

Quadruped motion in legged locomotion provides an outlook to explore both static and dynamic gaits.The leg contact of the quadruped with the environment is an impulsive contact with a non-smooth interaction.This impulsive force is resisted by the torques applied at the leg joints of the model, and hence, the realistic estimate of these resisting torques is vital for the stable operation of the robot.In the current study, the dynamic model of a planar two-legged mobile robot is formulated for an impact problem by utilizing the external impact model as proposed by Lee et al.(Modeling and analysis of internal impact for general classes of robotic mechanisms.In: Proceedings.IEEE/RSJ international conference on intelligent robots and systems, vol.3, pp.1955–1962, 2000 [1]).The impulse encountered during contact of the leg foot with the ground is utilized as the basis to compute the resisting forces at the joints in the model.These resisting joint forces due to impact can be used to decide the configuration of mobile robot leg during landing on the ground.From the simulation, it is established that the impact force on the joints is greatest when the orientation of the lower link of the leg is perpendicular to the contact environment.

Reconstruction of the pelvic region post the resection of pelvic bone sarcoma is vital for the rehabilitation and restoration of activities of daily living in patients. The prosthesis design should restore maximum functional outcomes for tumors that do not significantly decrease life expectancy. Currently, reconstruction methods use either bone grafts or prostheses. For tumors at regions such as the iliac wing and for young patients, there is minimal chance of bone grafts to remodel into the exact anatomy of the iliac wing. On the other hand, a customized pelvic prosthesis ensures restoration of the anatomical configuration and mechanical strength. A commercially available pelvic prosthesis is solid and is much stiffer than the bone leading to stress shielding effect and higher strains on the intact pelvic bone. This work proposes the design of a lightweight Ti6Al4V pelvic prosthesis for type-I resection due to a sarcoma at the iliac wing, which matches the exact anatomy of the resected pelvic bone. First, a compliance minimization problem subject to walking gait cycle loads with mass constraint equal to the mass of the resected iliac bone is solved using topology optimization. Then the density field from topology optimization is mapped into shell and lattice infills. Prosthesis designs with different lattice structures are subjected to a compression test simulation, and the heterogeneity of lattices on the structural performance of the prosthesis is studied. Thus, a lightweight prosthesis, similar in geometry, stiffness and mass to the natural iliac bone, is achieved with a decrease in stress shielding effect.