Mechanism and Machine Theory 116 (2017) 105–122 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory Research paper Defect-free optimal synthesis of crank-rocker linkage using nature-inspired optimization algorithms Ramanpreet Singh ∗ , Himanshu Chaudhary, Amit K Singh Department of Mechanical Engineering, Malaviya National Institute of Technology Jaipur, 302017, India a r t i c l e i n f o Article history: Received 24 February 2017 Revised 15 May 2017 Accepted 17 May 2017 Available online 25 May 2017 Keywords: Crank-rocker linkage TLBO algorithm Mechanism synthesis Path synthesis Knee-mechanism Defect rectification a b s t r a c t This paper proposes the synthesis of a human knee exoskeleton using the reduced num- ber of necessary and sufficient constraints. The proposed human knee exoskeleton con- sists of a defect-free crank-rocker mechanism capable of accurately moving its coupler point along the prescribed trajectory. For synthesizing the crank-rocker mechanism based on proposed reduced number of constraints, an optimization problem is formulated to synthesize the mechanism. An algorithm based on teaching-learning-based-optimization (TLBO) is presented to solve this highly nonlinear optimization problem. The optimiza- tion minimizes the error between generated and prescribed trajectory and simultaneously avoids any defect in the synthesized mechanism. The penalty method is used to manage all the constraints. Besides a realistic nontrivial example of human knee flexion/extension, a straight line trajectory is also considered to demonstrate the effectiveness of the refine- ment scheme in the optimal syntheses of planar crank-rocker linkage free from all defects. The optimization problem is solved using well-established nature-inspired algorithms such as genetic algorithm (GA), particle swarm algorithm (PSO), and teaching-learning-based- optimization (TLBO) algorithm. It is found that TLBO is computationally more efficient than other algorithms used here. Additionally, the proposed human knee exoskeleton model is experimentally validated for one gait cycle. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction An assembly of rigid bodies connected together to transform the specified motion is known as a linkage. A linkage is known as a mechanism when one or more links of the linkage are movable with respect to a stationary link. A Four-bar linkage is the simplest possible pin-jointed mechanism which is functionally flexible and topologically simple. It appears in various disguises for a variety of applications such as door-closing mechanisms, windshield wiping mechanisms, artificial human knee joint mechanism, and suspension systems of automobiles etc. [1]. In the design of a new mechanical system, kinematic synthesis of mechanism to fulfil desired motion characteristics is a challenge. Three areas are involved in kinematic synthesis, namely, type, number, and dimensional synthesis [2,3,45]. Kine- matic mechanism synthesis can be categorized as motion, path, and function generation. The fundamental approach for the path generation can be linkage coupler curve synthesis. There is a challenge of over-constrained problem in this approach, however, it can be resolved using a determined system of coupler-curve coefficient equations [54]. For the function genera- tion synthesis, an analytical method based on Fourier series components [51] can be employed, whereas, in case of motion ∗ Corresponding author. E-mail address: ramanpreet.gurdutta@hotmail.com (R. Singh). http://dx.doi.org/10.1016/j.mechmachtheory.2017.05.018 0094-114X/© 2017 Elsevier Ltd. All rights reserved.