Mapping between lists and Mapping Formats

Partition[connectionsOrder, 2, 1, {1, -1}, {}, Rule]

{"BASE" -> "HAA", "HAA" -> "HIP", "HIP" -> "HFE", "HFE" -> "THIGH",  
 "THIGH" -> "KFE", "KFE" -> "shank_fixed", "shank_fixed" -> "WHEEL",    
"WHEEL" -> "WHEEL_L"}

or

Rule @@@ Partition[connectionsOrder, 2, 1]

{"BASE" -> "HAA", "HAA" -> "HIP", "HIP" -> "HFE", "HFE" -> "THIGH",  
 "THIGH" -> "KFE", "KFE" -> "shank_fixed", "shank_fixed" -> "WHEEL",    
"WHEEL" -> "WHEEL_L"}

Also

EdgeRules @ PathGraph @ connectionsOrder

{"BASE" -> "HAA", "HAA" -> "HIP", "HIP" -> "HFE", "HFE" -> "THIGH",   
 "THIGH" -> "KFE", "KFE" -> "shank_fixed", "shank_fixed" -> "WHEEL",   
 "WHEEL" -> "WHEEL_L"}

BlockMap can do more of the work than you are allowing it to:

BlockMap[Apply[Rule], connectionsOrder, 2, 1]

{"BASE" -> "HAA", "HAA" -> "HIP", "HIP" -> "HFE", "HFE" -> "THIGH", 
 "THIGH" -> "KFE", "KFE" -> "shank_fixed", "shank_fixed" -> "WHEEL", 
 "WHEEL" -> "WHEEL_L"}