Modeling closed loop mechanisms is a necessity for the control and simulation of various systems like parallel robots, series-parallel hybrid robots, linkages, musculoskeletal systems etc. and pose a great challenge to rigid body dynamics algorithms. Many commercial software (e.g. ADAMS, RecurDyn, Simmechanics, V-Rep etc) and a very limited number of rigid body dynamics libraries (e.g. RBDL [2], DARTS [3], OpenSim [4,5]) provides this support. Solving the equations of motion for rigid body system with closed loops require resolution of loop closure constraints which are often solved via numerical procedures. This brings additional burden to these algorithms as they have to stabilize and control the loop closure errors additionally. In order to circumvent this issue, in recent work [1], a kinematics and dynamics library called Hybrid Robot Dynamics (HyRoDyn) is proposed, which provides a modular and analytical framework for resolving loop closure constraints in highly complex series-parallel hybrid robots. HyRoDyn only allows the analytical resolution of loop closure constraints for the parallel mechanisms that are known to its database.
    The progress has been made to extend the generality of the software so that it deals with the loop closure constraints numerically in a modular way. Now, the user can choose to solve a submechanism numerically in the HyRoDyn software. The user is expected to provide the loop constraints in a YAML Ain't Markup Language (YAML) file. To solve the loop closure constraints numerically, a cut joint technique is implemented. The software architecture involves the parsing of loop closure constraints defined by the user in YAML file. A new C++ class is implemented to handle the loop constraints nuemrically in a modular way. A couple of case studies is done for a single loop and multi-loop parallel kinematic chains. A case study of the hybrid series-parallel robot is also done and good results are obtained.
    The next step would be make the algorithm efficient and have insights into the trade-off between the modelling effort and generality of a multi-body simulation software. The work done in this thesis will be applied to the modelling and control of a complex biologically inspired series-parallel humanoid (RH5) or Recupera exoskeleton system or Autonomous Rough Terrain Excavator Robot (ARTER)

References:
[1] Kumar, S., Szadkowski, K. A. V., Mueller, A., and Kirchner, F.
(February 6, 2020). "An Analytical and Modular Software Work-
bench for Solving Kinematics and Dynamics of Series-Parallel Hybrid
Robots." ASME. J. Mechanisms Robotics. April 2020; 12(2): 021114.
doi.org/10.1115/1.4045941
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[3] Jain A. (2011) Constraint Embedding. In: Robot and Multibody Dynamics.
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