{"doi":"10.1115/1.4069154","title":"Kinematic Convex Combinations of Multiple Poses of a Bounded Planar Object Based on an Average-Distance Minimizing Motion Sweep","abstract":"Abstract This article deals with the computational kinematic geometry of bounded planar objects rather than that of infinitely large moving spaces. In this article, we present a new formulation for kinematic convexity based on an average-distance minimizing motion sweep of a bounded planar object. The resulting single-degree-of-freedom (DOF) motion sweep between two planar poses is represented as a convex combination in the configuration space defined by (x,y,z) where (x,y) is associated with the location of the centroid of the planar object and z=sinθ with θ being the angle of rotation. For three poses, a 2DOF motion sweep is developed that not only minimizes the combined average squared distances but also attains a convex combination representation so that existing algorithms for convex hull of points can be readily applied to the construction and analysis of kinematic convex hulls. This results in a new type of convex hull for planar kinematics such that its boundaries are defined by the average-distance minimizing sweeps of the bounded planar object.","journal":"Journal of Mechanisms and Robotics","year":2025,"id":539740,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":3,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9502,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2025-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":802040,"name":"Q. J. Ge","orcid":"0000-0001-5795-0128","position":1,"is_corresponding":false},{"id":802041,"name":"Márk Langer","orcid":"0000-0002-1234-1908","position":2,"is_corresponding":false},{"id":836067,"name":"Huan Liu","orcid":"0000-0002-0253-647X","position":0,"is_corresponding":true}],"reference_count":29,"raw_metadata":null,"created_at":"2026-07-19T02:52:34.520788Z","pmid":"40814295","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}